Method and apparatus for demodulating signals in a pulse oximetry system

ABSTRACT

A method and an apparatus measure blood oxygenation in a subject. A first signal source applies a first input signal during a first time interval. A second signal source applies a second input signal during a second time interval. A detector detects a first parametric signal responsive to the first input signal passing through a portion of the subject having blood therein. The detector also detects a second parametric signal responsive to the second input signal passing through the portion of the subject. The detector generates a detector output signal responsive to the first and second parametric signals. A signal processor receives the detector output signal and demodulates the detector output signal by applying a first demodulation signal to a signal responsive to the detector output signal to generate a first output signal responsive to the first parametric signal. The signal processor applies a second demodulation signal to the signal responsive to the detector output signal to generate a second output signal responsive to the second parametric signal. The first demodulation signal and the second demodulation signal both include at least a first component having a first frequency and a first amplitude and a second component having a second frequency and a second amplitude. The second frequency is a harmonic of the first frequency. The second amplitude is related to the first amplitude to minimize crosstalk from the first parametric signal to the second output signal and to minimize crosstalk from the second parametric signal to the first output signal.

REFERENCE TO PRIOR RELATED APPLICATION

This application claims priority from U.S. Provisional PatentApplication No. 60/043,620 filed Apr. 14, 1997 and entitled “METHOD ANDAPPARATUS FOR DEMODULATING SIGNALS IN A PULSE OXIMETRY SYSTEM.” Thisapplication also claims priority from U.S. patent application Ser. No.09/005,898 filed Jan. 12, 1998 and entitled “METHOD AND APPARATUS FORDEMODULATING SIGNALS IN A PULSE OXIMETRY SYSTEM”, U.S. Pat. No.5,919,134, issued on Jul. 6, 1999.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to the field of signal processing, and,more particularly, relates to the field of processing of signalsgenerated in a physiological monitoring system, such as, for example, ina system for measuring blood oxygen saturation using pulse oximetry.

2. Description of the Related Art

The present invention will be described herein in connection with apulse oximetry apparatus and a method, which are used to measure bloodoxygen saturation in a subject, such as, for example, a human patient.The teachings of the present invention can be used in other applicationswherein useable signal information is obtained in a noisy environment.

In an exemplary pulse oximetry apparatus and a corresponding method,blood oxygen saturation is determined by transmitting pulses ofelectromagnetic energy through a portion of a subject which has bloodflowing therein (e.g., through a finger, through an ear lobe, or otherportion of the body where blood flows close to the skin). In theexamples described herein, the pulses of electromagnetic energy compriseperiodic pulses of red light having wavelengths of approximately 660nanometers, for example, and periodic pulses of infrared light havingwavelengths of approximately 905 nanometers. As described, for example,in U.S. Pat. No. 5,482,036 and in U.S. Pat. No. 5,490,505, the pulses ofred light and the pulses of infrared light are applied with the sameperiodicity but in an alternating and non-overlapping manner. Inparticular, in preferred embodiments, the red pulses are active forapproximately 25% of each cycle and the infrared pulses are also activefor approximately 25% of each cycle. The red pulses are separated intime from the infrared pulses such that both pulses are inactive forapproximately 25% of each cycle between a red pulse and the nextinfrared pulse and both pulses are inactive for approximately 25% ofeach cycle between an infrared pulse and the next red pulse. (Althoughdescribed herein below in connection with pulses having 25% duty cycles,it should be understood by persons of skill in the art that the dutycycles of the pulses can be changed in some applications.) Afterpropagating through the portion of the subject, the red pulses and theinfrared pulses are detected by a detector which is responsive to lightat both wavelengths and which generates an electrical signal which has apredictable relationship to the intensity of the electromagnetic energyincident on the detector. The electrical signal is processed inaccordance with the present invention to provide a representation of theblood oxygen saturation of the subject.

In conventional time division multiplexing (TDM) demodulation that usesrectangular waves to drive the red and infrared LEDs, the conventionalprocess of demodulation using square waves can result in the aliasing ofthe ambient noise components that come close to the sidebands ofharmonics and the fundamental frequency of the rectangular waves, andthe noise components are thus collapsed into the output signal generatedby the demodulation. In particular, it is very difficult to avoidincluding harmonics of the line frequency in the demodulated outputsignal.

SUMMARY OF THE INVENTION

The present invention avoids the problems associated with conventionaldemodulation and separation of TDM signals. In particular, the presentinvention avoids the problem of aliasing of the ambient noise into thepassband of the system by selectively demodulating certain harmonics ofthe TDM signal. For example, in one embodiment, only two harmonics(e.g., the fundamental and the first harmonic) are demodulated. In otherembodiments, more harmonics are demodulated. The present inventionspecifically addresses solutions to problems caused by crosstalkresulting from filtering and also resulting from demodulating with onlycertain harmonics instead of demodulating with all harmonics as is doneusing conventional square wave demodulation. In a digital implementationof the present invention, the output of the photodetector is initiallysampled at a very high frequency (e.g., 46,875 Hz), and the signals aredecimated (where decimation is lowpass filtering followed by sample ratecompression) such that the final output signals are generated at arelatively low sampling rate (e.g., 62.5 Hz) which provides increasedresolution at the output. Thus, bandwidth is traded for resolution inthe output signal, thus increasing the signal to noise ratio.

One aspect of the present invention is an apparatus for measuring bloodoxygenation in a subject. The apparatus comprises a first signal sourcewhich applies a first input signal during a first time interval. Asecond signal source applies a second input signal during a second timeinterval. A detector detects a first parametric signal responsive to thefirst input signal passing through a portion of the subject having bloodtherein. The detector also detects a second parametric signal responsiveto the second input signal passing through the portion of the subject.The detector generates a detector output signal responsive to the firstand second parametric signals. A signal processor receives the detectoroutput signal. The signal processor demodulates the detector outputsignal by applying a first demodulation signal to a signal responsive tothe detector output signal to generate a first output signal responsiveto the first parametric signal and by applying a second demodulationsignal to the signal responsive to the detector output signal togenerate a second output signal responsive to the second parametricsignal. Each of the first demodulation signal and the seconddemodulation signal comprises at least a first component having a firstfrequency and a first amplitude and a second component having a secondfrequency and a second amplitude. The second frequency is a harmonic ofthe first frequency. The second amplitude is selected to be related tothe first amplitude to minimize crosstalk from the first parametricsignal to the second output signal and to minimize crosstalk from thesecond parametric signal to the first output signal. In one embodiment,the second amplitude is determined by turning off one of the first andsecond signal sources and measuring the crosstalk between one of theparametric signals and the non-corresponding output signal while varyingthe second amplitude. A second amplitude is selected that minimizes themeasured crosstalk.

Another aspect of the present invention is a method of minimizingcrosstalk between two signals generated by applying a first pulse and asecond pulse to measure a parameter. The first pulse and the secondpulse are applied periodically at a first repetition rate defining aperiod. The first pulse is generated during a first interval in eachperiod, and the second pulse is generated during a second interval ineach period. The second interval is spaced apart from the firstinterval. The first and second pulses produce first and secondparametric signals responsive to the parameter. The first and secondparametric signals are received by a single detector that outputs acomposite signal responsive to the first and second parametric signals.The method comprises the step of applying a first demodulation signal tothe composite signal to generate a first demodulated output signalwherein the first demodulation signal comprises at least a firstcomponent having a first frequency corresponding to the first repetitionrate. The first component has a first amplitude. The first demodulationsignal further comprises a second component having a second frequencythat is a harmonic of the first frequency. The second component has asecond amplitude which has a selected proportional relationship to thefirst amplitude. The method further includes the step of applying asecond demodulation signal to the composite signal to generate a seconddemodulated output signal. The second demodulation signal comprises thefirst component at the first frequency and the first amplitude andfurther comprises the second component at the second frequency and thesecond amplitude. At least one of the first and second components of thesecond demodulation signal has a selected phase difference with respectto the corresponding one of the first and second components of the firstdemodulation signal. The method further includes the steps of lowpassfiltering the first demodulated output signal to generate a firstrecovered output signal responsive to the first parametric signal; andlowpass filtering the second demodulated output signal to generate asecond recovered output signal responsive to the second parametricsignal.

Preferably, the selected phase difference is π. Also preferably, thefirst pulse and the second pulse are generally rectangular pulses havinga respective duty cycle. The rectangular pulses comprise a plurality ofsinusoidal components including a fundamental component corresponding tothe first frequency and a first harmonic component corresponding to thesecond frequency. The fundamental component has a fundamental componentamplitude and the first harmonic component has a first harmoniccomponent amplitude. The first harmonic component amplitude is relatedto the fundamental harmonic component amplitude by a firstproportionality value. The second amplitude of the second component ofthe first demodulation signal is related to the first amplitude of thefirst component of the first demodulation signal by a secondproportionality value which is approximately the inverse of the firstproportionality value.

The method in accordance with this aspect of the invention preferablyincludes the further steps of sampling the composite signal when neitherthe first pulse nor the second pulse is active to obtain a sampledsignal; and measuring the sampled signal to determine a noise level ofthe parametric signals.

In a further embodiment according to this aspect of the presentinvention, the method further includes the steps of performing atransform on the composite signal to generate a spectra of the compositesignal; sampling the spectra at a plurality of frequencies other than atpredetermined ranges of frequencies around the first frequency andaround harmonics of the first frequency; determining an average of themagnitudes of the sampled plurality of frequencies; and comparing theaverage to a selected threshold to determine whether the averagemagnitude exceeds the selected threshold.

Another aspect of the present invention is a method of demodulating acomposite signal generated by applying first and second periodic pulsesof electromagnetic energy to a system having a parameter to be measuredand by receiving signals responsive to the electromagnetic energy afterhaving passed through the system and being affected by the parameterbeing measured. The signals are received as a composite signal havingcomponents responsive to the first and second pulses. The methodcomprises the step of applying a first demodulation signal to thecomposite signal to generate a first demodulated signal. The firstdemodulation signal comprises a first component having a first frequencycorresponding to a repetition frequency of the first and second pulsesand comprises a second component having a frequency that is a harmonicof the first frequency. The first component has a first amplitude andthe second component has a second amplitude. The second amplitude has apredetermined relationship to the first amplitude. The predeterminedrelationship is selected to cause the first demodulated signal to havelow frequency components responsive only to the first pulse. The methodincludes the further step of lowpass filtering the first demodulatedsignal to generate a first output signal. The first output signal variesin response to an effect of the parameter on the electromagnetic energyreceived from the first pulse.

Preferably, the method in accordance with this aspect of the inventionincludes the further step of applying a second demodulation signal tothe composite signal to generate a second demodulated signal. The seconddemodulation signal has first and second components corresponding to thefirst and second components of the first demodulation signal. At leastone of the first and second components of the second demodulation signalhas a selected phase relationship with the corresponding one of thefirst and second components of the first demodulation signal. The methodincludes the further step of lowpass filtering the second demodulatedsignal to generate a second output signal. The second output signalvaries in response to an effect of the parameter on the electromagneticenergy received from the second pulse.

Another aspect of the present invention is a pulse oximetry system thatcomprises a modulation signal generator. The modulation signal generatorgenerates a first modulation signal that comprises a first pulse thatrepeats at a first repetition frequency. The first pulse has a dutycycle of less than 50%. The modulation signal generator generates asecond modulation signal comprising a second pulse that also repeats atthe first repetition frequency. The second pulse has a duty cycle ofless than 50%. The second pulse occurs at non-overlapping times withrespect to the first pulse. Each of the first and second pulsescomprises a plurality of components wherein a first component has afrequency corresponding to the repetition frequency and wherein a secondcomponent has a second frequency corresponding to twice the firstfrequency. The second component has an amplitude which has a firstpredetermined relationship to an amplitude of the first component. Afirst transmitter emits electromagnetic energy at a first wavelength inresponse to the first pulse; and a second transmitter emitselectromagnetic energy at a second wavelength in response to the secondpulse. A detector receives electromagnetic energy at the first andsecond wavelengths after passing through a portion of a subject andgenerates a detector output signal responsive to the receivedelectromagnetic energy. The detector output signal includes a signalcomponent responsive to attenuation of the electromagnetic energy at thefirst wavelength and a signal component responsive to attenuation of theelectromagnetic energy at the second wavelength. A first demodulatormultiplies the detector signal by a first demodulation signal andgenerates a first demodulated output signal. The first demodulationsignal comprises a first component having the first frequency and havinga first amplitude. The first demodulation signal also comprises a secondcomponent having the second frequency and having a second amplitude. Thesecond amplitude has a second predetermined relationship to the firstamplitude. The second predetermined relationship is approximatelyinversely proportional to the first predetermined relationship. A seconddemodulator multiplies the detector signal by a second demodulationsignal and generates a second demodulated output signal. The seconddemodulation signal comprises a first component having the firstfrequency and having the first amplitude. The second demodulation signalfurther comprises a second component having the second frequency andhaving the second amplitude. At least one component of the seconddemodulation signal has a selected phase relationship with acorresponding one component of the first demodulation signal.Preferably, the selected phase relationship is a π phase difference.

Another embodiment incorporates decimation before demodulation. In yetanother embodiment, a multi-channel demodulator, with or withoutpre-demodulation decimation is disclosed.

In yet another embodiment, an adaptive algorithm is used to control theoperation of pre-demodulation decimators and post-demodulationdecimators. The adaptive algorithm may control both the characteristicsof a lowpass filter in the decimator and the decimation rate provided bya signal rate compressor in the decimator.

Another embodiment of the invention is a method for selecting a samplerate that reduces the interference caused by ambient light.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be described below in connection with theaccompanying drawing figures in which:

FIG. 1 illustrates an exemplary block diagram of a representation of asignal processing system in accordance with the present invention usedto determine blood oxygen saturation in a subject;

FIG. 2 illustrates exemplary waveforms of the current through the LEDsin FIG. 1 and the resulting intensities of the red light and theinfrared light generated by the LEDs;

FIG. 3 illustrates a block diagram of the overall processing system inaccordance with the present invention;

FIG. 4 illustrates a frequency spectra of the first modulation signalM₁(t) for n=0, 1, 2, . . . , where the horizontal axis representsfrequency and the vertical axis represents the energy in the DC andharmonic components of the signal;

FIG. 5 illustrates an exemplary spectrum of the first and secondharmonics of the present invention when the fundamental frequency isselected to be 316.7 Hz in comparison to the fundamental and harmonicsof conventional 60 Hz power;

FIG. 6 illustrates the effect of the value of B on the measured signaloutput Ŝ₂(t) responsive to the red modulation pulses as the value of Bis varied while the infrared modulation pulses are off;

FIG. 7 illustrates a preferred embodiment of the present inventionimplemented in a digital processing system;

FIG. 8 illustrates a detailed block diagram of the demodulation portionof the present invention;

FIG. 9 illustrates a detailed block diagram of the modulation portion ofthe present invention;

FIG. 10 illustrates the red drive waveform and the infrared drivewaveform generated by the modulation portion of FIG. 9;

FIG. 11 illustrates the demodulation waveforms generated by thedemodulation portion of FIG. 8;

FIG. 12 illustrates a method of time domain sampling the digitaldetection signal during the times when both the red pulses and theinfrared pulses are off to obtain information regarding the level ofambient noise;

FIG. 13 illustrates a block diagram of a system that performs the timedomain sampling of FIG. 12;

FIG. 14 illustrates a method of frequency domain sampling to determinethe noise floor at frequencies other than the signal frequencies;

FIG. 15 illustrates a block diagram of a system that performs thefrequency domain sampling of FIG. 14;

FIG. 16 illustrates a block diagram of the overall processing system inaccordance with a pre-demodulation decimation embodiment of the presentinvention;

FIG. 17 illustrates a block diagram of a multi-channel processing systemin accordance with a pre-demodulation decimation embodiment of thepresent invention;

FIG. 18 illustrates a block diagram of an adaptive multi-channelprocessing system in accordance with a pre-demodulation decimationembodiment of the present invention;

FIG. 19 illustrates a flowchart of a method for choosing the modulationfrequency and decimation rate in order to minimize the affects ofambient light; and

FIG. 20 is a graph to be used in connection with graphical method fordesigning a demodulation system to minimize interference due to ambientlight.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 illustrates an exemplary block diagram of a representation of asignal processing system 100 in accordance with the present inventionused to determine blood oxygen saturation in a subject, such as, forexample, a human subject. In the example presented, the measurements areperformed on a portion of the subject, such as a finger 102 illustratedin FIG. 1. An LED modulation circuit 104 drives a pair of back-to-backlight emitting diodes (LEDs) 106, 108 by applying a periodic signal tothe two light emitting diodes 106, 108. The LED 106 is selected to emitelectromagnetic energy in the red visible light range, and has awavelength of, for example, approximately 660 nanometers. The LED 108 isselected to emit electromagnetic energy in the infrared range, and has awavelength of, for example, approximately 905 nanometers. The LEDmodulation circuit 104 supplies current in alternating directions sothat the two LEDs 106, 108 are activated one at a time. In particular,as illustrated by a current waveform 120 in FIG. 2, current is firstapplied in a forward direction with respect to the red LED 106 during afirst time interval 122 having a duration τ. Thereafter, no current isapplied to either LED during a second time interval 124 having a likeduration τ. Then, current is applied in a forward direction with respectto the infrared LED 108 during a third time interval 126, also having aduration τ. Then, no current is applied to either LED during a fourthtime interval 128 having a like duration τ. Thereafter, the current isagain applied in the forward direction for the red LED 106 during afifth time interval 130 which corresponds to the first time interval122. It can be seen that the overall cycle repeats with a period ofduration T equal to 4τ. The red LED 106 emits light only when thecurrent is applied in the forward direction with respect to the red LED106. Thus, as illustrated by a red intensity waveform 132, the red LED106 emits light as a pulse 134 during the first time interval 122 and asa pulse 136 during the fifth time interval 130, and so on. The redpulses repeat with a periodicity equal to T. Similarly, the infrared LED108 emits infrared light only when the current is applied in the forwarddirection with respect to the infrared LED 108. Thus, as illustrated byan infrared intensity waveform 140, the infrared LED 108 emits infraredlight as a pulse 142 during the third interval 126. A next infraredpulse 144 occurs at an interval T after the infrared pulse 142. Thus,the infrared pulses also repeat with a periodicity equal to T. It can beseen that the red pulses and the infrared pulses each have a duty cycleof 25%, and the red pulses and the infrared pulses are separated byintervals of one-fourth of each period T (i.e., the beginning of onepulse occurs an interval τ after the end of the previous pulse).

As further illustrated in FIG. 1, the electromagnetic energy pulses fromthe red LED 106 and the infrared LED 108 are applied to the finger 102.A detector 150 is positioned to receive the electromagnetic energy afterthe energy has passed through a portion of the finger 102. The detector150 is selected to be responsive to both the red light and the infraredlight and to generate an output signal responsive to the intensity ofthe energy received from each source. An exemplary current output signalfrom the detector 150 is represented by a waveform 152 in FIG. 2. Asillustrated, the detector signal waveform 152 comprises a first pulse154 responsive to the first red pulse 134, a second pulse 156 responsiveto the infrared pulse 142 and a third pulse 158 responsive to the secondred pulse 136. During the time between the first pulse 154 and thesecond pulse 156, the detector signal waveform 152 comprises noise 160,and during the time between the second pulse 156 and the third pulse158, the detector signal waveform 150 comprises noise 162. The signalpulses 154, 156 and 158 also include noise superimposed thereon.Although shown as repeating noise, it should be understood that thenoise varies with time. For example, noise caused by ambient light willvary with a periodicity corresponding to the 50 Hz or 60 Hz powerfrequency and their harmonics, particularly when the ambient light isprovided by fluorescent lights which generate significant noise at thefirst harmonic (i.e., 100 Hz or 120 Hz) and the third harmonic (i.e.,200 Hz or 240 Hz).

The output of the detector 150 is applied as an input to a signalprocessor block 170 which processes the detector signal and generates afirst signal Ŝ₁(t) responsive to the detected intensity of the red lightincident on the detector 150 and generates a second signal Ŝ₂(t)responsive to the detected intensity of the infrared light incident onthe detector 150. As illustrated, the signal processing block 170 issynchronized with the LED modulator 104 via a set of control lines 180.As will be discussed below, the control lines 180 advantageouslycommunicate signals which provide timing information that determineswhen to activate the red LED 106 and when to activate the infrared LED108.

FIG. 3 is a pictorial representation of a model of an exemplary systemwhich incorporates the present invention. The red LED 106 provides alight intensity represented as I_(RD), and the infrared LED 108 providesa light intensity represented as I_(IR). The effects of turning the LEDs106, 108 on and off on periodic bases are modeled by a first multiplieror modulator 190 which applies a first modulation signal M₁(t) to thered light intensity to generate a modulated red signal I_(RDMOD)(t) andby a second multiplier or modulator 192 which applies a secondmodulation signal M₂(t) to the infrared light intensity to generate amodulated infrared signal I_(IRMOD)(t). The modulated light red signaland the modulated infrared signal are applied to the finger 102, orother body portion, as described above. The finger 102 has blood flowingtherein and is represented in FIG. 3 as a block 102. The blood in thefinger 102 has a volume and scattering components which vary throughouteach cardiac cycle. The blood carries oxygen and other materialstherein. The oxygen content is a function of both the blood volume andthe concentration of the oxygen in the blood volume. The concentrationof the oxygen in the blood volume is generally measured as blood oxygensaturation for reasons which are described in full in theabove-identified issued U.S. Pat. Nos. 5,482,036 and 5,490,505. Asfurther described in the two referenced patents, the blood oxygensaturation is determined by comparing the relative absorption of the redlight and the infrared light in the finger 102. The comparison iscomplicated by the noise caused by movement, ambient light, lightscattering, and other factors.

In FIG. 3, a pair of signals S₁(t) and S₂(t) represent the effect of thetime-varying volume and scattering components of the blood in the finger102 on the red light and the infrared light, respectively, passingthrough the finger 102 from the LEDs 106, 108 to the detector 150. Thered light signal portion S₁(t) is caused by the variable attenuation ofthe red light passing through the finger 102. The infrared light signalportion S₂(t) is caused by the variable attenuation of the infraredlight passing through the finger 102. To show the effect of the variableattenuations, the signal portion S₁(t) is illustrated as being appliedto a first attenuation modulator 191 which multiplies the signal S₁(t)by the modulated red output I_(RDMOD)(t) of the first modulator 190.Similarly, the infrared light signal portion S₂(t) is illustrated asbeing applied to a second attenuation modulator 193 which multiplies thesignal S₂(t) by the modulated infrared output I_(IRMOD)(t) of the secondmodulator 192. The outputs of the first and second attenuationmodulators 191, 193 are provided to the receiving photodetector 150. Thephotodetector 150 is modeled as adder 194 and an adder 196. The outputsof the first and second attenuation modulators 191, 193 are provided tothe adder 194 to generate a composite signal M(t) where:

M(t)=S ₁(t)M ₁(t)+S ₂(t)M ₂(t).  (1)

The signal M(t) from the adder 194 is provided to the adder 196 wherethe signal M(t) is added to a signal n(t) which represents a compositenoise signal caused by ambient light, electromagnetic pickup, and thelike, which are also detected by the photodetector 150. The output ofthe adder 196 is a signal M′(t)=M(t)+n(t) which includes noisecomponents as well as the signal components. The noise componentsinclude DC components and harmonics of the power line frequency thatappear in the ambient light. In addition, as will be discussed in moredetail below, the signal M′(t) may also include noise at higherfrequencies caused, for example, by other devices such aselectrocauterization equipment, or the like.

The M′(t) signal output of the third adder 196 (i.e., the output of thedetector 150) is applied to the input of the signal processing block170. Within the signal processing block 170, the signal M′(t) is firstpassed through a fixed gain amplifier 197 and then through an analogbandpass filter 198. The analog bandpass filter 198 has a passbandselected to pass signals in the range of 20 Hz to 10,000 Hz. Thus, theanalog bandpass filter 198 removes a significant portion of the noisebelow 10 Hz. The signal components responsive to the blood oxygensaturation are frequency shifted by the operation of the two modulationsignals M₁(t) and M₂(t) and are passed by the analog bandpass filter198.

In the preferred embodiment, the output of the analog bandpass filter198 is sampled by an analog-to-digital converter 199 and convertedtherein to digital signals. For example, the signals are preferablysampled at 46,875 samples per second. The output of theanalog-to-digital converter 199 is a signal MF(k).

The signal MF(k) is provided as a first input to a first demodulatingmultiplier 210. The signal MF(k) is also provided as a first input to asecond demodulating multiplier 212. A first demodulating signal D₁(k) isprovided as a second input to the first demodulating multiplier 210, anda second demodulating signal D₂(k) is provided as a second input to thesecond demodulating multiplier 212. The output of the first demodulatingmultiplier 210 is provided as an input to a first lowpass filter 220,and the output of the second demodulating multiplier is provided as aninput to a second lowpass filter 222. The bandwidths of the lowpassfilters 220, 222 are preferably approximately 10 Hz.

The output of the first lowpass filter 220 is a signal Ŝ₁(t), which, asdiscussed below, is an estimate of the signal S₁(t). The output of thesecond lowpass filter 222 is a signal Ŝ₂(t), which, as discussed below,is an estimate of the signal S₂(t). As will be shown below, theselection of the first demodulating signal D₁(k) and the seconddemodulating signal D₂(k) in accordance with the present inventionsubstantially reduces or eliminates the effects of noise in the twooutput signals Ŝ₁(t) and Ŝ₁(t) and also substantially reduces oreliminates crosstalk between the two signals.

In the preferred embodiment of the present invention, the sample ratesof the outputs of the lowpass filter 220 and the lowpass filter 222 arecompressed by respective sample rate compressors 221 and 223. Inparticular, the sample rate compressors 221, 223 reduce the sample rateby 750 to a sample rate of, for example, 62.5 Hz to provide an outputwhich can be further processed in accordance with the methods andapparatuses described in the above-referenced patents. The sample ratecompressions which occur in the sample rate compressors 221, 223 reducethe rate at which the output signals Ŝ₁(t) and Ŝ₂(t) need to beprocessed while maintaining the sample rate well above the 0-10 Hzfrequency content of the signals of interest. The outputs of the filters220, 222, or the sample rate compressors 221, 223, if included, areprovided on respective output lines 224 and 226.

In order to facilitate an understanding of how the present inventionoperates in demodulating the output signal MF(k) from theanalog-to-digital converter 199, the modulation signals M₁(t) and M₂(t)will first be described in terms of their frequency components. Oneskilled in the art will appreciate that the modulation signals M₁(t) andM₂(t) can each be represented as a Fourier cosine series expansion$\left( {{e.g.},\quad {\sum\limits_{n = 0}^{\infty}{a_{n}{\cos \left( {n\quad \omega \quad t} \right)}}},\quad {{{where}\quad \omega} = {2{\pi/T}}}} \right)$

representing the fundamental and harmonic frequencies of the rectangularsignal pulses. One skilled in the art will understand that the Fourierseries expansion includes phases; however, by suitably selecting thetime origin, the phases are set to zero. A component which is 180° outof phase with a corresponding component will advantageously berepresented by a minus sign before the coefficient.

FIG. 4 illustrates a frequency spectra of the first modulation signalM₁(t) for n=0, 1, 2, . . . , where the horizontal axis representsfrequency, with the energy in the DC component along the vertical axisand increasing harmonics of the fundamental frequency along thehorizontal axis. The length of each component of M₁(t) along thevertical axis represents the energy E(n) in each component of thefrequency spectra. The first component to the right of the vertical axisis at the fundamental frequency (i.e., 1/T), which is designated hereinas f₀; however, it should be understood that the fundamental frequencyf₀ corresponds to n=1. The second component to the right of the verticalaxis is the first harmonic f₁ (i.e., n=2), which has a frequency whichis twice the fundamental frequency. The third component to the right ofthe vertical axis is the second harmonic f₂ (i.e., n=3), which has afrequency which is three times the fundamental frequency. The componentsto the right of the second harmonic are numbered accordingly. (Note,other conventions identify the fundamental frequency as the firstharmonic, and designate the second harmonic as the frequency that istwice the fundamental frequency. The identification of the fundamentalfrequency as f₀ is used in the discussion that follows.)

In FIG. 4, a modulation envelope 230 is shown in dashed lines. Themodulation envelope 230 represents the magnitudes of the fundamental andthe harmonics of the signal M₁(t). The shape of the envelope isdetermined by the modulation signal M₁(t) which, for a repeatingrectangular pulse train starting at time t=0 and having a normalizedamplitude of 1, can be expressed as: $\begin{matrix}{{M_{1}(t)} = {\frac{\tau}{T}{\sum\limits_{n = 0}^{\infty}{\sin \quad {c\left( \frac{n\quad \tau}{T} \right)}\cos \quad \left( \frac{2\pi \quad {nt}}{T} \right)}}}} & (2)\end{matrix}$

Where sinc is the function (sin πx)/πx (i.e.,sinc(nτ/T)=sin(nπτ/T)/(nπτ/T)). In the example shown, τ=¼T. (Note thatfor sampled signals, the envelope is more accurately represented assinα/sinβ; however, as well known in the art, for the frequencies ofinterest, the sinc function is a suitable approximation.) Thus, thefrequency spectra has nulls at n=4, n=8, n=12, and so on, correspondingto the third harmonic f₃, the seventh harmonic f₇, the eleventh harmonicf₁₁, and so on. Note that Equation 2 is an idealized form of theequation for M₁(t), and that in general: $\begin{matrix}{{M_{1}(t)} = {\frac{\tau}{T}{\sum\limits_{n = 0}^{\infty}{a_{n}{sinc}\frac{n\quad \tau}{T}^{{- j}\quad \omega_{0}{nt}}}}}} & (3)\end{matrix}$

where a_(n) is a complex number. In the discussion that follows, thevalues of a_(n) are assumed to be real numbers only.

A similar frequency spectra (not shown) for the modulation signal M₂(t)is determined by the expression: $\begin{matrix}{{M_{2}(t)} = {\frac{\tau}{T}{\sum\limits_{n = 0}^{\infty}{\left( {- 1} \right)^{n}{{sinc}\left( \frac{n\quad \tau}{T} \right)}\cos \quad \left( \frac{2\pi \quad {nt}}{T} \right)}}}} & (4)\end{matrix}$

An envelope for the frequency spectra of second modulation signal M₂(t)will have the same magnitudes; however, it should be understood thatbecause of the (−1)^(n) term in the expression for M₂(t), thefundamental f₀ and every even harmonic (i.e., f₂, f₄, etc.) are 180° outof phase with the corresponding harmonic of the first modulation signalM₁(t).

In FIG. 3, the analog-to-digital converter 199 converts the signal M′(t)to a sequence of sampled digital values MF(k) at a sampling rate of, forexample, 46,875 samples per second. As discussed above, the firstdemodulating multiplier 210 multiplies the output MF(k) of the converter199 by the first demodulating signal D₁(k) to generate the first outputsequence Ŝ₁(k), and the second demodulating multiplier 212 multipliesthe output MF(k) by the second demodulating signal D₂(k) to generate thesecond output sequence Ŝ₂(k). The multiplication by the multipliers 210,212 can also be expressed as follows:

Ŝ ₁(k)=LP[MF(k)D ₁(k)]  (5)

and

 Ŝ ₂(k)=LP[MF(k)D ₂(k)]  (6)

where LP is the transfer function of the lowpass filter 220 and of thelowpass filter 222. If, for simplicity, the noise is assumed to be zero,then:

M′(t)=S ₁(t)M ₁(t)+S ₂(t)M ₂(t)  (7)

Therefore:

Ŝ ₁(k)=LP[[S ₁(k)M ₁(k)+S ₂(k)M ₂(k)]D ₁(k)]  (8)

and thus

Ŝ ₁(k)=LP[[S ₁(k)M ₁(k)]D ₁(k)+[S ₂(k)M ₂(k)]D ₁(k)]  (9)

Similarly:

Ŝ ₂(k)=LP[[S ₂(k)M ₂(k)]D ₂(k)+[S ₁(k)M ₁(k)]D ₂(k)]  (10)

Since LP is a linear operator, the right-hand side of Equations 9 and 10can be split into two terms. The first term on the right-hand side ofeach of Equations 9 and 10 above is the desired signal portion of theequation, and the second term on the right-hand side of each of theequations is the crosstalk portion. Thus, in order to reduce thecrosstalk to zero, the second term of each of Equations 9 and 10 is setto zero:

LP[S ₂(k)M ₂(k)D ₁(k)]=0  (11)

and

LP[S ₁(k)M ₁(k)D ₂(k)]=0  (12)

By setting the second terms to zero, Equations 9 and 10 reduce to:

Ŝ ₁(k)=LP[S ₁(k)M ₁(k)D ₁(k)]  (13)

and

Ŝ ₂(k)=LP[S ₂(k)M ₂(k)D ₂(k)]  (14)

One goal of the present invention is to select the demodulating signalsD₁(k) and D₂(k) to satisfy Equations 11 and 12 to thereby reduceEquations 9 and 10 to Equations 13 and 14. This is accomplished byutilizing Equations 2 and 3 to simplify the two equations by selectivelyusing components of the two modulating signals M₁(t) and M₂(t) togenerate the demodulating sequences D₁(k) and D₂(k).

In order to simplify the discussion, Equation 2 can be rewritten as:$\begin{matrix}{{M_{1}(t)} = {\sum\limits_{n = 1}^{\infty}{{E(n)}\cos \quad \left( {n\quad \omega \quad t} \right)}}} & (15)\end{matrix}$

where E(n) is the sinc envelope for the fundamental frequency f₀ (n=1)and the harmonics f₁ (n=2), f₂ (n=3), and so on, where cos(nωt)represents the cosine term cos(2πnt/T), where ω=2π/T. (Note, asdiscussed above, for discrete sampled signals, the actual envelope ofE(n) is a sinα/sinβ function; however, for the frequencies of interest,the sinc function is a suitable representation.)

As discussed above, the DC term (n=0) does not need to be consideredbecause of the operation of the filter 198, and the analog-to-digitalconverter 199, as well as the action of the demodulation, which shiftany unwanted DC or low frequency signals having a frequency less thanapproximately 10 Hz (hereinafter near-DC signals) to higher frequenciesbefore lowpass filtering. As a further simplification, the magnitude ofthe fundamental term in Equation 15 is normalized to a value of 1 (i.e.,E(1)=1). Note that the normalization results in the need for a scalefactor, which will be discussed below. Thus, Equation 15 becomes:

M ₁(t)=cos ωt+a cos 2ωt+b cos 3ωt+c cos 4ωt+ . . .  (16)

The demodulation signal D₁(t) is defined as:

D ₁(t)=cos ωt+B cos 2ωt  (17)

For reasons set forth below, only the first two cosine terms are needed.

Similarly, the second modulating signal M₂(t) becomes:

M ₂(t)=−cos ωt+a cos 2ωt−b cos 3ωt+c cos 4ωt+ . . .  (18)

and the second demodulating signal D₂(t) is defined as:

D ₂(t)=−cos ωt+B cos 2ωt  (19)

Note that the signs of the fundamental and odd harmonics in Equation 18are 180° out of phase with the corresponding terms in Equation 16.

Note, as will be developed more fully below, by including only thefundamental (cos ωt) and the first harmonic (cos 2ωt) in each of thedemodulation signals, only the signals proximate to the fundamental andfirst harmonic need to be considered. By eliminating higher harmonics,the effects of the higher harmonics of the power line frequency are alsoeliminated in the output signals generated by the present invention.

Assume that the filter 198 and the analog-to-digital converter 199 donot affect the magnitude of the signal MF(k) with respect to M′(t) forthe frequencies having significant energy. Therefore, starting withEquation 7 above, M′(t) can be written as:

M′(t)=S ₁(t)[cos ωt+a cos 2ωt+b cos 3ωt+ . . . ]

+S ₂(t)[−cos ωt+a cos 2ωt−b cos 3ωt+ . . . ]  (20)

When the first demodulating multiplier 210 multiplies M′(t) by D₁(t),the terms on the right-hand side of Equation 20 are multiplied by theterms on the right-hand side of Equation 17. Thus:

M′(t)D ₁(t)=S ₁(t)[cos ωt+a cos 2ωt+b cos 3ωt+ . . . ][cos ωt+B cos 2ωt]

+S ₂(t)[−cos ωt+a cos 2ωt−b cos 3ωt+ . . . ][cos ωt+B cos 2ωt]  (21)

The term S₁(t)[cos ωt+a cos 2ωt+b cos 3ωt+ . . . ][cos ωt+B cos 2ωt] isthe signal term which is to be preserved, and the term S₂(t)[−cos ωt+acos 2ωt−b cos 3ωt+ . . .][cos ωt+B cos 2ωt] is the crosstalk term to beeliminated.

Expanding the crosstalk term from Equation 21, generates:

crosstalk=S ₂(t)[−cos² ωt−B cos ωt cos 2ωt+a cos 2ωt cos ωt+aB cos² 2ωt

−b cos 3ωt cos ωt−bB cos 3ωt cos 2ωt+ . . . ]  (22)

Using the identity, cos(x)cos(y)=½[cos(x+y)+cos(x−y)], the crosstalkterm from Equation 22 becomes:

crosstalk=S ₂(t)[−½(cos 2ωt+1)+((a−B)/2)[cos 3ωt+cos ωt]

+(aB/2)[cos 4ωt+1]−(b/2)[cos 4ωt+cos 2ωt]

−(bB/2)[cos 5ωt+cos ωt]+ . . . ]  (23)

The remaining terms in Equation 23 will all have a factor of cos ωt orhigher. Thus, Equation 23, when fully expanded only includes near-DCterms:

crosstalk _(DC) =LP[S ₂(t)[(aB/2)−½]]  (24)

where S₂(t) corresponds to the infrared portion of the originalplethysmograph signal which has a bandwidth of interest of approximately0 to 10 Hz. Any components present above 10 Hz will be eliminated by theaction of the lowpass filter 220. Thus, it can be seen that only thesignals of interest are folded back to DC or near-DC. By using thelowpass filter 220, the DC terms and near-DC terms can be isolated sothat only the DC terms and near-DC terms of the crosstalk are presentedat the output of the lowpass filter 220. Thus, in order to eliminate thecrosstalk, the crosstalk terms in Equation 24 need to be set to zero:

LP[S ₂(t)[aB/2−½]]=0  (25)

Thus:

B=1/a  (26)

The result in Equation 26 can also be expressed using a geometricinterpretation of vector projection (i.e., dot products) of S₂(t) andS₁(t) wherein the projection of S₂(t) onto D₁(t) is equal to zero andthe projection of S₂(t) onto D₂(t) is maximized. In other words, expressS₁(t), S₂(t), D₁(t) and D₂(t) as vectors of samples in an n-dimensionalsample space (e.g., S₁(t) is represented as a vector S₁ of samplesS₁(k)). For example, in a preferred embodiment, n=148, and thus S₁,S_(2, D) ₁ and D₂ are vectors of 148 samples each. The first crosstalkterm is S₁·D₂. The second crosstalk term is S₂·D₁. The first signaloutput is S₁·D₁. The second signal output is S₂·D₂. Select the vectorsD₁ and D₂ to drive the crosstalk terms to zero.

The relationship in Equation 26 also works to preserve the signal term.In particular, the signal term in Equation 21 can be expanded andlowpass filtered in the same manner as the crosstalk term to obtain:

signal=Ŝ ₁(t)=LP[S ₁(t)[(aB/2)+½]]  (27)

Using the relationship from Equation 26, then Equation 27 becomes:

signal=Ŝ ₁(t)=LP[S ₁(t)[(a/2a)+½]=LP[S ₁(t)]=S ₁(t)  (28)

It can be readily shown that the same relationship holds for thecrosstalk term and the signal term for the signal S₂(t) by defining thesecond demodulation signal D₂(t) as:

D ₂(t)=−cos ωt+B cos 2ωt  (b 29)

and multiplying M₂(t) by D₂(t). After expanding the crosstalk and signalterms and eliminating the terms above 10 Hz, it can be shown that byselecting B=1/a, the crosstalk term is canceled and the signal termS₂(t) is recovered.

From the foregoing, it can be seen that by choosing the relationshipbetween the magnitude of B as the reciprocal of a, then the crosstalkterms are eliminated and the signal terms are preserved. Note thatneither A nor B is an absolute value. As set forth in Equation 16, a isthe magnitude of the cos2ωt term of M₁(t) when the magnitude of thecosωt term of M₁(t) is normalized to 1. Similarly, from Equation 17, Bis the magnitude of the cos 2ωt term of D₁(t) when the cos ωt term ofD₁(t) is normalized to 1.

It should be understood that both D₁(t) and D₂(t) can include higherharmonic terms; however, such additional terms could result in increasedsensitivity to the noise of fluorescent lights and the like because ofthe harmonics of the 60 Hz power line frequency (or the 50 Hz power linefrequency in other countries). For example, FIG. 5 illustrates anexemplary spectrum of the first and second harmonics of the presentinvention when the fundamental frequency is selected to be 316.7 Hz.Thus, the first harmonic frequency is 633.4 Hz. Note that the variationsin the signals caused by blood flow throughout a cardiac cycle causesthe fundamental and harmonics of modulation frequency to be surroundedby sidebands representing the frequency content of the plethysmograph.For example, in FIG. 5, the first and second harmonics are at 316.7 Hzand 633.4 Hz, ±10 Hz.

As further illustrated in FIG. 5, the conventional 60 Hz power linefrequency has harmonics at 120 Hz, 180 Hz, 240, etc. Thus, the nearestharmonics of the power line frequency to the first harmonic of thepresent invention are at 300 Hz and 360 Hz, and the nearest harmonics ofthe power line frequency to the second harmonic of the present inventionare 600 Hz and 660 Hz. Similarly, if used in a country having a 50 Hzpower line frequency, the nearest harmonics to the first harmonic of thepresent invention are 300 Hz and 350 Hz, and the nearest harmonics tothe second harmonic of the present invention are 600 Hz and 650 Hz. Evenif the power frequency were to vary by up to 1.5 percent, the noisegenerated by the ambient light from fluorescent lamps, or the like,would not be at the first and second harmonic frequencies of the presentinvention. The fundamental frequency has thus been selected to avoidpower line caused ambient noise at the first and second harmonicfrequencies.

The foregoing discussion assumed that the filter 198 did notsignificantly affect the amplitude of the filtered signal. If the filter198 does have an affect on the amplitude, then B will be a constanttimes the value of B determined above:

B=k/a  (30)

where k depends on the relative attenuation of the first harmonic andthe second harmonic through the filter 198.

Although the value of the coefficient B can be calculated as set forthabove, the calculations may be complicated if the filter 198 or themodulators 190, 192 introduce phase changes which cause the calculationsto be performed on complex numbers. For example, if the modulationsignals M₁(t) and M₂(t) are not rectangular waves which have 25% dutycycles and which are precisely 180° out of phase, as illustrated herein,then the coefficients of the frequency components of the modulationsignals may be complex to account for the phase relationships, and thus,the coefficients of the demodulation signals may be complex.

As illustrated in FIG. 6, the value of B can also be determinedempirically by performing a initial measurement with one channel (i.e.,either the red pulse or the infrared pulse turned off) and minimizingthe crosstalk. In particular, during the initial measurement, thewaveform 140 in FIG. 2 is set to a continuous zero value so that noinfrared pulses are generated. Thus, the detector 150 (FIG. 1) receivesonly the light generated by the red LED 106. Thus, M₂(t) is set to zero,and Equation 10 for Ŝ₂(t) becomes:

Ŝ ₂(t)=LP[S ₁(t)M ₁(t)D ₂(t)]  (31)

It can be seen that Ŝ₂(t) includes only a crosstalk portion, which canbe measured on the output from the second lowpass filter 222. Thus, byvarying the value B while monitoring the magnitude or the RMS(root-mean-squared) value of the output signal Ŝ₂(t), a minimummagnitude Ŝ₂(t)_(min) for the output signal Ŝ₂(t) can be found whichcorresponds to the best value B_(BEST) for B. In an ideal system, thebest value for B corresponds to a zero value for the output signalŜ₂(t); however, in a real environment, the best value of B maycorrespond to a non-zero value for Ŝ₂(t) (i.e., a minimum error forŜ₂(t)). It should be understood that the value of B_(BEST) can also bedetermined by tuning off the red LED 106 and varying B while monitoringŜ₁(t) until Ŝ₁(t) is minimized.

From the foregoing, it can be seen that the effect of the modulationsignals D₁(t) and D₂(t) is to shift the DC or near-DC noise terms up infrequency while shifting the signals of interest at the harmonics backto DC or near-DC, which in effect interchanges the noise spectra and thesignal spectra so that the noise spectra can be eliminated by the actionof the lowpass filters 220, 222, leaving only the signals of interest.

FIG. 7 illustrates a preferred embodiment of the present invention whichimplements the functions described above in a digital system.Preferably, the digital system comprises a digital signal processor (notshown), and the blocks described herein comprise data structures withinthe digital signal processor and software routines that implement theprocesses described below. In particular, the present inventioncomprises an LED demodulation block 300 which receives a digitalconfiguration signal on a bus 310, a clock signal on a line 312 and adigital detector signal on a bus 314 as inputs. The digitalconfiguration signal bus 310 provides a way to change the configurationof the LED demodulation block 300 to accommodate different LEDs anddifferent detection algorithms. Preferably, the clock signal on the line312 is a 46,875 Hz (46.875 kHz) square wave signal which is used tosynchronize the timing functions of the present invention The digitaldetector signal on the line 314 is the output of the analog-to-digitalconverter 199. The analog-to-digital converter 199 is connected to theoutput of the detector 150 (via the amplifier 197 and the filter 198)and samples the output of the detector 150 at 46,875 samples per secondto provide a stream of sampled digital values of the red light andinfrared light incident on the detector 150.

The LED modulation block 300 generates a demodulated red signal outputon a bus 340 and generates a demodulated infrared signal output on a bus342. The demodulated red signal output is passed through the low passfilter 220 and is output therefrom as the signal Ŝ₁(t). The demodulatedinfrared signal output is passed through the low pass filter 222 and isoutput therefrom as the signal Ŝ₂(t). As further illustrated in FIG. 8,the LED demodulation block 300 comprises a modulo-M block 350, an LEDdemodulation state table block 352, the first demodulating multiplier210 and the second demodulating multiplier 212.

The modulo-M block 350 receives the main 46,875 Hz clock signal on theline 312 as one input and receives a MODULUS signal on a bus 354 as asecond input. The bus 354 forms a portion of the configuration bus 310.The modulo-M block 350 divides the clock signal by the MODULUS signaland generates a RESIDUE signal (described below) on a bus 356 which isprovided as one input to the LED modulation state table block 352. TheLED modulation state table block 352 also receives the configurationsignals on the configuration bus 310.

The LED demodulation state table is responsive to the residue signal andthe configuration signals to generate the first demodulating signalD₁(t) on a bus 360 and to generate the second demodulating signal D₂(t)on a bus 362. The first demodulating signal D₁(t) is provided as oneinput to the first demodulating multiplier 210, as described above. Thesecond demodulating signal D₂(t) is provided as one input to the seconddemodulating multiplier 212, as described above. The first demodulatingmultiplier 210 and the second demodulating multiplier 212 receive thedigital detector signal on the line 314 as respective second inputs. Thedemodulating multipliers 210, 212 multiply the digital detector signalby the first demodulating signal D₁(t) and the second demodulatingsignal D₂(t), respectively, to generate a demodulated red signal and ademodulated infrared signal on the buses 340 and 342, respectively.Because the outputs of the two demodulating multipliers 210 and 212include the terms cos ωt, cos 2ωt, and higher, the demodulated signalson the buses 340 and 342 are provided as respective inputs to the lowpass filters 220 and 222 to pass only the near-DC terms, as discussedabove. The outputs of the lowpass filters 220 and 222 on the buses 344and 346, respectively, are the Ŝ₁(t) signal and the Ŝ₂(t) signal whichcontain only the near-DC terms, which, in accordance with the discussionpresented above represent the original input signals S₁(t) and S₂(t)with the unwanted noise substantially reduced or eliminated. The twosignals Ŝ₁(t) and Ŝ₂(t) are then applied to computation circuitry (notshown) which computes the blood oxygen saturation and othercardiographic parameters in a manner described in the above-cited U.S.Pat. Nos. 5,482,036 and 5,490,505.

The residue signal generated as the output from the modulo-M block 350is a multiple bit signal that counts from 0 to MODULUS-1. In thepreferred embodiment described herein, MODULUS has a value of 148. Thus,the RESIDUE output of the modulo-M block 350 counts from 0 to 147. TheRESIDUE output of the modulo-M block 350 is a number that is provided asthe input to the LED demodulation state table block 352. As illustratedin FIG. 9, the RESIDUE output on the bus 356 corresponds to the signal180 in FIG. 1 and is also provided to the input of an LED modulationstate table block 370 which, together with an LED driver circuit 372,comprise the modulation block 104 (FIG. 1) which generates the drivesignals to the red LED 106 and the infrared LED 108. As described above,the red LED 106 and the infrared LED 108 generate the modulation signalsM₁(t) and M₂(t), respectively, which effectively operate as carriers forthe plethysmograph waveform to be measured. In particular, asillustrated by a red drive timing waveform 374 and by a infrared drivetiming waveform 376 in FIG. 10, the modulation state table block 370generates a red signal pulse 378 during the time when the RESIDUE signalincrements from 0 to 36. Then, the modulation state table block 370generates neither a red signal pulse nor an infrared signal pulse duringthe time when the RESIDUE signal increments from 37 to 73. Then, themodulation state table block 370 generates the infrared signal pulse 380during the time when the RESIDUE signal increments from 74 to 110. Then,the modulation state table block 370 again generates neither a redsignal pulse nor an infrared signal pulse during the time when theRESIDUE signal increments from 111 to 147. The RESIDUE signal thenresets to 0 and the process repeats continuously.

The red signal pulse 378 and the infrared signal pulse 380 from themodulation state table block 370 are provided as inputs to the LEDdriver circuit 372 which turns on the red LED 106 when the red signalpulse 376 is active and turns on the infrared LED 108 when the infraredsignal pulse 378 is active by generating the current waveform 120illustrated in FIG. 2. The circuitry for converting the red signal pulse376 and the infrared signal pulse 378 to the bi-directional currentpulses of the waveform 120 is conventional and does not need to bedescribed herein.

In the preferred embodiment, the LED demodulation state table block 352implements demodulation equations which generally correspond to theEquations 17 and 19 described above. In particular, the LED demodulationstate table block 352 receives the RESIDUE as one input to the statetable and steps through the state table based upon the current value ofthe RESIDUE. The LED demodulation state table block 352 generates twooutput values for each value of the RESIDUE, wherein the first outputvalue is the first demodulation signal D₁(t) on the signal bus 360, andthe second output value is the second demodulation signal D₂(t) on thesignal bus 362.

In particular, the LED demodulation state table block 352 implements thefollowing forms of the demodulation signal D₁(t) and the D₂(t)equations: $\begin{matrix}\begin{matrix}{{D_{1}(t)} = \quad {- {{SCL}\left( {{\cos \quad\left\lbrack {2\pi \quad {t\left( \frac{{R - 18.5 - {{HW}\quad \Delta}}\quad}{Modulus} \right)}} \right\rbrack} +} \right.}}} \\{\quad \left. {{HWD}\left( {\cos \left\lbrack {4\pi \quad {t\left( \frac{{R - 18.5 - {{HW}\quad \Delta}}\quad}{Modulus} \right)}} \right\rbrack} \right)} \right)}\end{matrix} & (32)\end{matrix}$

and $\begin{matrix}\begin{matrix}{{D_{2}(t)} = \quad {- {{SCL}\left( {{\cos \quad\left\lbrack {2\pi \quad {t\left( \frac{{R - 18.5 - {{HW}\quad \Delta}}\quad}{Modulus} \right)}} \right\rbrack} -} \right.}}} \\{\quad \left. {{HWD}\left( {\cos \left\lbrack {4\pi \quad {t\left( \frac{{R - 18.5 - {{HW}\quad \Delta}}\quad}{Modulus} \right)}} \right\rbrack} \right)} \right)}\end{matrix} & (33)\end{matrix}$

In Equations 32 and 33, the value SCL is a scale factor which determinesthe magnitudes of the two demodulation signals and which is used tocompensate for the normalization discussed above and to compensate forother factors, such as, for example, non-ideal rectangular pulses. Themethod of determining the scale factor will be set forth below. In oneparticularly preferred embodiment, the value of SCL is 2.221441469. Thevalue HWD is a hardware distortion factor, which corresponds to thevalue of B discussed above. The determination of the value B wasdescribed above, and will be described again below in connection withthis preferred embodiment. In one particularly preferred embodimentwhere the pulses applied to the red LED 106 and the infrared LED 108 areidealized rectangular waves having 25% duty cycles, the value of HWD canbe calculated to be 1.414213562. This ideal value for HWD can bedetermined by recognizing that the value of the coefficient A for thecos 2ωt terms in Equations 16 and 18 is determined by the sinc function.When the coefficient of the cos ωt term is normalized to 1, as in thetwo equations, then the value of the coefficient a is equal to {squareroot over (2)}/2. Thus, the ideal value for B (i.e., HWD) is {squareroot over (2+L )}. Of course, the actual value of the coefficient B, andthus HWD, will vary when the red pulses and the infrared pulses are nottrue rectangular waves. Since, in actual embodiments, the pulses willhave finite rise times and fall times, the optimum value of HWD ispreferably found empirically in the manner described below.

The value 18.5 in Equations 32 and 33 is used to align the demodulationwaveforms with the modulation waveforms so that the peak of the cosinefunctions corresponds to the midpoints of each of the modulationwaveforms. The value HWΔ is a hardware delay factor which may be neededin certain embodiments to compensate for delays in the analogprocessing, the digital processing or both, which cause the demodulationsignals D₁(t) and D₂(t) to be out of phase with the modulation signalsM₁(t) and M₂(t). In an ideal environment, the value of the hardwaredelay factor is 0. However, in one particularly preferred embodiment,the value of the hardware delay factor is 39. The modulus was describedabove and is basically the number of steps in each period of thewaveforms. In the embodiment described herein, the modulus is 148. Thevalue R is the RESIDUE, which varies from 0 to modulus-1, and thus, inthe preferred embodiment, R varies from 0 to 147.

In operation, the clock signal on the line 312 causes the modulo-M block350 to generate the RESIDUE signal, as described above. The RESIDUEvalue is applied to the LED modulation block 104 which generates themodulation signals M₁(t) and M₂(t), as described above. The RESIDUEvalue is also applied to the LED demodulation state table block 352which generates a new value for D₁(t) and a new value for D₂(t) for eachnew RESIDUE value. Thus, 148 values of D₁(t) and D₂(t) are generated foreach complete cycle. Because the clock signal is operating at 46,875 Hz,the modulation signals M₁(t) and M₂(t) and the demodulation signalsD₁(t) and D₂(t) have a fundamental frequency of 316.722973 Hz, which asduscussed above, does not correspond to any harmonic of conventional 50Hz or 60 Hz power line frequencies.

The HWΔ(hardware delay factor) value, the HWD (hardware distortionfactor) value and the SCL (scaling factor) value are found empiricallyas follows. First, the ideal values of the hardware delay the factor,the hardware distortion factor and the scale factor are applied to theEquations 32 and 33 in the LED demodulation state table block 352 (i.e.,HWΔ=0, HWD=1.414213562, and SCL=2.221441469). To determine the optimumvalue of the hardware delay factor, the second modulation signal M ₂(t)is set to a constant value of zero (i.e., the infrared LED is maintainedin its OFF state). The red LED pulses are applied as set forth above,and the digital detector output signal from the analog-to-digitalconverter is monitored and compared to the modulation signal M₁(t). Therelative delay between the beginning of the modulation signal M₁(t) andthe detection of the beginning of the responsive output from theanalog-to-digital converter is the optimum hardware delay factor (HWΔ)value. In one exemplary embodiment, the optimum value of the hardwaredelay factor is 39.

After determining the value of the hardware delay factor and applying itto Equations 32 and 33, the ideal value of the hardware distortionfactor and the ideal value of the scale factor are applied to the twoequations. Again, with the red LED pulses applied to the red LED 106 andno pulses applied to the infrared LED, the value of the hardwaredistortion factor is slowly varied from its ideal value while the DCcomponent of the demodulated infrared signal output on the line 342 ismonitored. The value of the hardware distortion factor is varied untilthe measured DC component is minimized, and the value of the hardwaredistortion factor corresponding to the minima DC component is selectedas the optimum value for the hardware distortion factor.

Next, with the value of the hardware delay factor and the value of thehardware distortion factor set to their respective optimum values, asdetermined above, the value of the scale factor (SCL) is initially setto 1. Again, with the modulation system generating pulses only to thered LED 106, the DC component of the demodulated red signal output onthe line 340 is measured. In addition, the difference in amplitudebetween the on state and the off state of the digital detector signalfrom the filter 198 is measured. The ratio of the measured amplitudedifference to the measured DC component of the demodulated red signaloutput is selected as the optimum value for the scale factor.

An exemplary demodulation waveform D₁(t) is illustrated by a waveform400 in FIG. 11 and an exemplary demodulation waveform D₂(t) isillustrated by a waveform 402 in FIG. 11. The demodulation waveforms inFIG. 11 are illustrated with the hardware delay factor set to 0 in orderto align the waveforms with the modulation waveforms in FIG. 10. Itshould be understood that when the hardware delay factor is non-zero,the demodulation waveforms in FIG. 11 will be shifted in phase withrespect to the modulation waveforms in FIG. 10.

Although described above in connection with the variation of theamplitude of the first harmonic component of the demodulation signals inorder to minimize the crosstalk, it should be understood that therelative amplitude of the second harmonic component of the demodulationsignals with respect to the amplitude of the fundamental component ofthe demodulation signals is determined by the relationship of theamplitude of the first harmonic component of the modulation signals tothe amplitude of the fundamental component of the modulation signals.The relationship of the amplitude of the first harmonic component of themodulation signals depends in part upon the duty cycles of themodulation signals. If the modulation duty cycles are varied, theamplitude of the first harmonic component of the modulation signalschanges. Thus, the crosstalk may also be minimized by holding theamplitudes of the components of the demodulation signals constant whilevarying the duty cycles of the modulation signals. One skilled in theart will appreciate that other variations in the modulation anddemodulation signals may also be used to minimize the crosstalk betweenthe two output signals.

A plurality of signals S₁, S₂, S₃ . . . S_(n) can be demodulated and thecrosstalk between signals reduced to a minimum by application of theforegoing invention to more than two signals.

Additional information can advantageously be derived from the digitizeddetection signal on the bus 314 and can be used to provide indicationsregarding the reliability of the demodulated signals generated asdescribed above. In particular, although the present system is capableof demodulating the Ŝ₁(t) signal and the Ŝ₂(t) signal in the presence ofsignificant ambient noise from light and other sources, it is possiblethat the level of the ambient noise is sufficiently high to affect thedemodulated signals. FIGS. 12 and 13 illustrate a time domain method andsystem for determining the ambient noise level, and FIGS. 14 and 15illustrate a frequency domain method and system for determining theambient noise level.

As illustrated in FIG. 12, the digital detection signal 152 is sampledby a sample signal represented by a waveform 500, which comprises aplurality of sampling pulses 502. The sampling pulses 502 are timed tooccur during the intervals between the red pulses 134, 136 and theinfrared pulses 142, 144 when no red light and no infrared light shouldbe detected by the detector 150 (FIG. 1). Thus, any energy detectedduring the sample intervals is primarily caused by ambient light andother noise sources. As illustrated, the sampling pulses 502 preferablyoccur at the approximate midpoint of each interval between the red andinfrared pulses.

As illustrated in FIG. 13, the digital detection signal bus 314 isprovided as an input to a time domain sampler 520. The time domainsampler 520 also receives the RESIDUE signal on the bus 356 as a secondinput. The time domain sampler is responsive to the RESIDUE signal tosample the digital detection signal at times when the value of theRESIDUE signal corresponds to the quiescent times of the red pulses 134,136 and the infrared pulses 142, 144. As described above, the red pulses134, 136 are generated when the RESIDUE signal has values between 0 and36, and the infrared pulses are generated when the RESIDUE signal hasvalues between 74 and 110. Thus, assuming no hardware delay, thesampling pulses 502 are preferably generated, for example, when theRESIDUE signal has a value of 55 and when the RESIDUE signal has a valueof 129, which positions the sampling pulses at the approximate midpointsof the quiescent intervals between the pulses. As discussed above, theactual system has a hardware delay caused by processing times. Thus, ifthe system has a hardware delay factor of, for example, 39, the samplingpulses 502 are shifted in time to occur when the RESIDUE signal has avalue of 94 and a value of 20 (168 modulo₁₄₈). The sample times used bythe time domain sampler 520 are advantageously determined byconfiguration signals received via the digital configuration bus 310,described above. For example, the time domain sampler 520 can beinitially set to sample at RESIDUE signal values of 55 and 129, and thevalue of the hardware delay value factor (HWΔ) communicated by thedigital configuration bus 310 is added to both values to shift thesample to the correct sample interval.

As illustrated in FIG. 14, a detection signal spectra 550 includes thetwo frequency components corresponding to the fundamental and firstharmonic of the modulation signal at 316.7 Hz and 633.4 Hz,respectively. The spectra 550 further includes the fundamental andmultiple harmonics of the 60 Hz power line frequency. In addition, thespectra 550 includes noise at a multitude of frequencies which may becaused by various sources. One particularly troublesome source of noiseencountered in pulse oximetry systems is an electrocauterization device,which uses a high frequency electrical current to make surgicalincisions and to cauterize the surrounding blood vessels at the sametime. Although primarily high frequency noise sources, such devices alsogenerate significant noise at lower frequencies because of arcing. Whenan electrocauterization device is operated close to a pulse oximeterdetector, the noise generated by the device can overwhelm the signalsgenerated by the pulse oximetry detector. In other words, the noisefloor can be greater than the detectable signal from the pulse oximetrydetector.

It is desirable to detect when the noise floor is too high so that thepulse oximetry system can indicate that the demodulated signals may notbe reliable. In order to determine the level of the noise floor, thepresent invention samples the spectra 550 to determine the content ofthe frequency components detected at frequencies other than thefundamental and harmonic frequencies of the modulation signals. Inparticular, as illustrated by a sample control signal 560 in FIG. 14,the portions of the spectra 550 which do not include the fundamental andharmonics of the modulation signal are sampled. Thus, in the preferredembodiment, the magnitudes of the spectra at 316.7 Hz, 633.4 Hz, 950.1Hz, etc., are not sampled. Furthermore, because a band of frequenciesaround the fundamental and harmonics of the modulation signal alsoinclude significant information caused by the modulation of the redpulses and the infrared pulses by the changes in blood flow during eachcardiac cycle. Thus, as illustrated in FIG. 14, in the preferredembodiment, a band of frequencies surrounding the fundamental andharmonic frequencies of the modulation signals (i.e., the sidebandsdiscussed above) are not included in the samples. For example, a band ofat least ±10 Hz around each of the fundamental and harmonic frequenciesis not included in the samples.

The intensities at the sampled frequencies are averaged, and an outputsignal is generated which represents the average intensity of the noisesignals. Other portions (not shown) of the digital processing systemadvantageously monitor the average intensity of the noise signals, and,if the average intensity exceeds a selected threshold based upon thesize of the measured plethysmograph, then the demodulated output signalsfrom the system are considered as being unreliable and should not beused.

FIG. 15 illustrates a preferred embodiment of a system that determinesthe noise floor, as described above. The system of FIG. 15 includes aFast Fourier Transform block 600 which receives a plurality of samplesfrom the digitized detector bus 314 and generates a transformed outputon a bus 610. The transformed output on the bus 610 represents thespectra of the samples. In the preferred embodiment, a sufficient numberof samples are taken to represent approximately 44 milliseconds of dataso that at least two cycles of the 60 Hz power are included within thesamples. For example, approximately 1,024 samples can be taken duringthe 44 millisecond interval at a sample rate of approximately 23.4 kHz(e.g., one-half the system timing rate). The spectra for a44-millisecond interval are provided as inputs to a spectral sampler 620which eliminates the samples in the ±10 Hz bands around the fundamentaland harmonic frequencies of the modulation signals. The output of thespectral sampler 620 is provided on a bus 630 and is thereby provided asan input to an averager 640. The averager 640 averages the sampled noisespectra which it receives and provides an averaged output on a bus 650.The averaged output on the bus 650 represents the noise floor and isprovided to other portions of the digital processing system where it iscompared to the selected threshold to determine whether the noise flooris excessive. The threshold is not necessarily fixed, but is dependenton the strength of the plethysmograph, which in turn depends upon theperfusion of blood in the body portion being measured.

The embodiment of FIG. 15 can also advantageously be used to determinewhether the ambient noise is primarily at 60 Hz, corresponding to powerline frequencies in the United States and Canada, or at 50 Hz,corresponding to power line frequencies in Europe. The foregoingmodulation frequency of 316.7 Hz is selected to avoid the harmonics ofthe 60 Hz power line frequency as well as the 50 Hz power linefrequency. If a significant shift in the power line frequency isdetected such that aliasing of the ambient noise occurs at thefrequencies of interest, then the modulation frequency can be changed todisplace the modulation harmonics farther from the harmonics of thepower line frequency, such as, for example, by changing the 46,875 Hzsampling frequency, or by changing the modulus.

Pre-Demodulation Decimation

For convenience, the previous embodiments do not show the signal MF(k)being decimated before demodulation. However, as discussed in moredetail below, the signal MF(k) can advantageously be decimated prior todemodulation. The pre-demodulation decimation technique can reduce thecomputational burden required to perform the demodulation operations,primarily because the decimated sample rate is lower than the original(undecimated) sample rate. Computation can also be reduced because, aswill be seen, the numerical sequences used in the demodulator are, insome circumstances, shorter than the sequences given in Equations 32 and33. Pre-demodulation decimation is a generalization of the previousembodiments and reduces to the previous embodiments when thepre-demodulation decimation rate is one.

FIG. 16 is a pictorial representation of a system that incorporatespre-demodulation filtering and decimation. FIG. 16 is similar to FIG. 3,and like numbers refer to like elements in the two figures. FIG. 16shows the first modulator 191 having a signal input S₁(t) and amodulation input M₁(t). The second modulator 193 has a signal inputS₂(t) and a modulation input M₂(t). The pair of signals S₁(t) and S₂(t)represent the effect of the time-varying volume and scatteringcomponents of the blood in a finger (or other body part) on the redlight and the infrared light, respectively, passing through the finger.The red light signal portion S₁(t) is caused by the variable attenuationof the red light passing through the finger 102 (shown in FIG. 1). Theinfrared light signal portion S₂(t) is caused by the variableattenuation of the infrared light passing through the finger 102. Theoutputs of the first and second modulators 191, 193 are provided to thereceiving photodetector 150. The photodetector 150 is modeled as anadder 194 and an adder 196. The outputs of the first and secondmodulators 191, 193 are provided to the adder 194 to generate acomposite signal M(t) where:

M(t)=S ₁(t)M ₁(t)+S ₂(t)M ₂(t).  (34)

The output signal M(t) from the adder 194 is provided to an adder 196where a signal n(t) is added to the signal M(t). The signal n(t)represents a composite noise signal caused by ambient light (includingDC and harmonics of the power line frequency), electromagnetic pickup,and the like, which are also detected by the photodetector 150. Inaddition, the signal n(t) may also include noise at higher frequenciescaused, for example, by other devices such as electrocauterizationequipment, or the like. The output of the adder 196 is a signalM′(t)=M(t)+n(t) which includes noise components as well as the signalcomponents.

The M′(t) signal output of the adder 196 (i.e., the output of thedetector 150) is applied to the input of a signal processing block 1600.Within the signal processing block 1600, the signal M′(t) is firstpassed through the amplifier 197 and then through the analog bandpassfilter 198. The analog bandpass filter 198 provides anti-aliasing andremoval of low frequency noise and DC. The filter 198 has a passbandselected to pass signals in the preferred range of 20 Hz to 10,000 Hz.The analog bandpass filter 198 removes a significant portion of thenoise below 20 Hz. The signal components responsive to the blood oxygensaturation are frequency shifted by the operation of the two modulationsignals M₁(t) and M₂(t) and are passed by the analog bandpass filter198.

In one embodiment, the output of the analog bandpass filter 198 issampled by the analog-to-digital converter 199 and converted therein todigital signals. In one embodiment, the signals are sampled at 46,875samples per second. The digital signals from the analog-to-digitalconverter 199 are provided as inputs to a lowpass digital filter 1620.Output signals from the digital filter 1620 are provided to a samplerate compression block 1622 that reduces (compresses) the sample rate bya decimation rate R₁. The lowpass digital filter 1620 and sample ratecompressor 1622 together comprise a decimator 1621 (decimation compriseslowpass filtering followed by sample rate compression). The digitalfilter 1620 provides anti-aliasing filtering and the sample ratecompression block 1622 preferably operates at a sampling rate of atleast twice the highest frequency of interest as determined by thedigital filter 1620. In one embodiment, the sample rate compressionblock 1622 reduces the sample rate by a factor of R₁=37, correspondingto the number of samples during the period τ as illustrated in FIG. 10.The output of the sample rate compression block 1622 provides one sampleper time period τ and thus four samples per time period T. The output ofthe sample rate compression block 1622 is a signal MF(k) (where k is adiscrete index) which comprises approximately 1,266 samples per second.

The signal MF(k) is provided as a first input to a first mixer 1624. Thesignal MF(k) is also provided as a first input to a second mixer 1626. Afirst demodulating signal D₁(k) is provided as a second input to thefirst mixer 1624, and a second demodulating signal D₂(k) is provided asa second input to the second mixer 1626. The output of the first mixer1624 is provided as an input to a first lowpass filter 1630, and theoutput of the second mixer is provided as an input to a second lowpassfilter 1640. The bandwidths of the lowpass filters 1630, 1640 arepreferably approximately 10 Hz. The signal MF(k) is also provided as afirst input to a noise channel mixer 1628. A noise demodulating signalD₀(k) is provided as a second input to the noise channel mixer 1628. Theoutput of the noise channel mixer 1628 is provided to an input of a lowpass filter 1650. The output of the low pass filter 1650 is provided toa sample rate compression block 1652. The output of the sample ratecompression block 1652 is an estimate of the noise n(t). The output ofthe lowpass filters 1630 is provided to an input of a sample ratecompressor 1632 and the output of the lowpass filter 1640 is provided toan input of a sample rate compressor 1642. The lowpass filter 1630 andthe sample rate compressor 1632 together comprise a decimator 1631. Thelowpass filter 1640 and the sample rate compressor 1642 togethercomprise a decimator 1641,

The output of the decimator 1631 is a signal Ŝ₁(k), which, as discussedbelow, is an estimate of the signal S₁(k). The output of the decimator1641 is a signal Ŝ₂(k) , which, as discussed below, is an estimate ofthe signal S₂(k). As will be shown below, the selection of the firstdemodulating signal D₁(k) and the second demodulating signal D₂(k) inaccordance with the present invention can reduce or eliminate theeffects of noise in the two output signals Ŝ₁(k) and Ŝ₂(k) and alsoreduce or eliminate crosstalk between the two signals.

The decimators 1632, 1642 decimate by a decimation rate R₂. In apreferred embodiment, the decimators 1632, 1642 decimate by a decimationrate R2=20 to a sample rate of, for example, 63.3 Hz to provide adecimated output which can be further processed in accordance with themethods and apparatuses described in the above-referenced patents. Thedecimations which occur in the decimators 1632, 1642 reduce the rate atwhich the output signals Ŝ₁(k) and Ŝ₂(k) need to be processed whilemaintaining the sample rate well above the 10 Hz frequency content ofthe signals of interest. The outputs of the decimators 1632, 1642 areprovided on respective output lines 1634 and 1644.

Decimating the signal MF(k) prior to demodulation, although not anapproximation technique, can be simplified by assuming that each desiredsignal S_(i)(t) does not change appreciably during each period τ. Inmany applications it is reasonable to assume that the desired signalsS₁(t) and S₂(t) will not change significantly during the time interval τshown in FIG. 2. One skilled in the art will recognize that a sufficientcondition for this assumption is that the highest significant frequencycomponents in S₁(t) and S₂(t) are much lower than the modulationfrequency. In the pulse-oximetry application the highest frequency ofinterest is typically around 10 Hz, which is far below the 316.7 Hzfundamental of the modulation. Since n(t) is not a desired signal, nosuch assumption is necessary for n(t). Thus, while n(t) may varyerratically over a modulation cycle, the signals S₁(t) and S₂(t) do not.Therefore, it is possible to perform pre-demodulation decimation thathas little effect on S₁(t) and S₂(t) but may shape n(t) into n′(t). Themeasured signal is decimated by a factor R₁=Q (where Q is the number ofsamples in a time period τ) and then demodulated.

Assuming R₁=Q, then the spectral domain representation of the signalMF(k) at the output of the sample rate compression block 1622 is givenby (approximately): $\begin{matrix}\begin{matrix}{{{MF}(f)} = \quad {{\frac{1}{T}{\sum\limits_{n = {- \infty}}^{\infty}\left\lbrack {{S_{1}\left( {f - \frac{n}{T}} \right)} + {\left( {- 1} \right)^{n}{S_{2}\left( {f - \frac{n}{T}} \right)}}} \right\rbrack}} +}} \\{\quad {\frac{4}{T}{\sum\limits_{m = {- \infty}}^{\infty}{n^{\prime}\left( {f - \frac{4m}{T}} \right)}}}}\end{matrix} & (35)\end{matrix}$

Since the sample rate compression block 1622 decimates at the same rateas the number of samples per period τ, the decimation removes any τdependence in the expression for MF(f). The frequency components indexedby m increase four times faster than the frequency components indexed byn. This occurs because the modulated signals S₁(t) and S₂(t), which areindexed by n, occur in only one fourth of the samples, but the noisen(t), which is indexed by m, occurs in every sample.

The demodulation operation can be performed either in the frequency orthe time domain. A method for frequency domain demodulation of thesignal MF(k) can be obtained by rewriting Equation 35 as:

MF(f)= . . . MF ⁻²(f)+MF ⁻¹(f)+MF ₀(f)+MF ₁(f)+MF ₂(f)+ . . .  (36)

where

MF ⁻²(f)=[S ₁(f)+S ₂(f)]/T

MF ⁻¹(f)=[S ₁(f)−S ₂(f)]/T

MF ₀(f)=[S ₁(f)+S ₂(f)+4n′(f)]/T

MF ₁(f)=[S ₁(f)−S ₂(f)]/T

MF ₂(f)=[S ₁(f)+S ₂(f)]/T

MF ₃(f)=[S ₁(f)−S ₂(f)]/T

MF ₄(f)=[S ₁(f)+S ₂(f)+4n′(f)]/T  (37)

Where n′(k) is the decimated noise signal n(t). Estimates for the signalS₁(f) can be obtained by shifting the spectra of MF₁(f) and MF₂(f) by−1/T and −2/T, respectively, and then dividing the sum of the resultantby 2. Likewise, S₂(f) can be obtained by dividing the difference of theresultant spectra by 2. In other words:

Ŝ₁(f)=MF ₁(f−1/T)+MF ₂(f−2/T)

Ŝ₂(f)=MF ₁(f−1/T)−MF ₂(f−2/T)  (38)

Demodulation in the time domain is a more elegant method for obtainingS₁(k) and S₂(k). Time domain demodulation is obtained by using thefrequency shift property of the Fourier transform given by:

F(ω+ω₀)⇄e ^(−jω) ₀ ^(t) f(t)  (39)

According to Equation 39, the frequency domain terms MF_(i)(f) arerelated by a time shift in the time domain and this property can be usedto generate the demodulation sequences D₀−D₂. A more completedevelopment of this process (for the general case of N channels) isprovided in Equations 42-50 below and in the text accompanying thoseequations. For the present case, where N=2, using equations 42-50 gives:

 D ₀(k)=0,1,0,1, . . .

D ₁(k)=1,−0.5,0,−0.5, . . .

D ₂(k)=0,−0.5,1,−0.5, . . .  (40)

The sequences shown in Equation 40 are repeating sequences of the fourvalues shown. Thus, the demodulation waveforms are no more than shortrepeating sequences of simple coefficients. Since the samples MF(k) aretime domain sequences, demodulation simply involves multiplying thesamples MF(k) by the sequences in Equation 40. For example, the sequenceof coefficients D₀(k)=(0, 1, 0, 1, . . . ) is provided to the multiplier1628 to demodulate the signal MF(k) and produce the estimate of n(k).Similarly, the sequence of coefficients D₁(k)=(1,−0.5,0,−0.5, . . . ) isprovided to the multiplier 1624 to demodulate the signal MF(k) andproduce the estimate of S₁(k).

Multiple Channel Modulation and Demodulation

The two-channel pre-demodulation decimation technique described in theprevious section can be extended to multi-channel systems having morethan two desired signals. FIG. 17 illustrates an expansion of thetwo-channel modulator into a multi-channel modulator/demodulator. FIG.17 shows the first modulator 191 and the second modulator 193 as shownin FIG. 16. Further, FIG. 17 shows a third modulator 1701 and an N^(th)modulator 1702. The signal input S₁(t) and a modulation input M₁(t) areprovided to the first modulator 191. The signal input S₂(t) and amodulation input M₂(t) are provided to the second modulator 193. Asignal input S₃(t) and a modulation input M₃(t) are provided to thethird modulator 1701. A signal input S_(N)(t) and a modulation inputM_(N)(t) are provided to the N^(th) modulator 1702.

The photodetector 150 is modeled as an adder 194 and an adder 196. Theoutputs of the modulators 191, 193, 1701, and 1703 are added together inthe adder 194, to generate a composite signal M(t) where:

M(t)=S ₁(t)M ₁(t)+S ₂(t)M ₂(t)+S ₃(t)M ₃(t)+ . . . +S _(N)(t)M_(N)(t)  (41)

The signal M(t) from the adder 194 is provided to the adder 196 wherethe signal M(t) is added to the signal n(t) which represents a compositenoise signal caused by ambient light, electromagnetic pickup, and thelike, which are also detected by the photodetector 150. The output ofthe adder 196 is the signal M′(t)=M(t)+n(t), which includes the noisecomponents as well as the signal components.

The M′(t) signal output of the adder 196 (i.e., the output of thedetector 150) is applied to the input of the signal-processing block1700. Within the signal-processing block 1700, the signal M′(t) is firstpassed through an amplifier 197 and then through the analog bandpassfilter 198. The analog bandpass filter 198 provides anti-aliasing andremoval of low frequency noise and DC. The desired signal components inthe signals S_(i)(t) are frequency shifted by the operation of themodulation signals M_(i)(t) and are passed by the analog bandpass filter198.

The output of the analog bandpass filter 198 is sampled by theanalog-to-digital converter 199 and converted therein to digital signalsand provided to an input of the lowpass digital filter 1620. Outputsignals from the digital filter 1620 are provided to a sample ratecompression block 1622, which reduces the sample rate by a decimationfactor R₁. Together, the digital filter 1620 and the sample ratecompression block 1622 comprise a decimator 1621. The output of thesample rate compression block 1622 is a signal MF(k). The signal MF(k)is provided as: the first input to the first mixer 1624; the first inputto the second mixer 1626; a first input to a third mixer 1710; a firstinput to an N Th mixer 1712; and a first input to a noise channel mixer1713. A first demodulating signal D₁(k) is provided as a second input tothe first mixer 1624. A second demodulating signal D₂(k) is provided asa second input to the second mixer 1626. A third demodulating signalD₃(k) is provided to the third mixer 1710. A fourth demodulating signalD_(N)(k) is provided to the N^(th) mixer 1712. A noise demodulatingsignal D₀(k) is provided to the noise channel mixer 1713. The outputs ofthe mixers 1624, 1626, 1710, 1712, and 1713 are provided as respectiveinputs of the lowpass filters 1630, 1640, 1720, 1730, and 1740. Theoutputs of the lowpass filters 1630, 1640, 1720, 1730, and 1740 areprovided as respective inputs of the decimators 1632, 1642, 1721, 1731and 1741. Each of the decimators 1632, 1642, 1721, 1731 and 1741 reducesthe sample rate by a decimation rate R₂.

The output of the sample rate compressor 1632 is a signal Ŝ₁(k), which,as discussed below, is an estimate of the signal S₁(k). Likewise, theoutput of the sample rate compressor 1642 is an estimate of S₂(t), theoutput of the sample rate compressor 1721 is an estimate of the signalS₃(t), the output of the sample rate compressor 1731 is an estimate ofthe signal S_(N)(t), and the output of the sample rate compressor 1741is an estimate of the signal n(t).

As will be shown below, the selection of the demodulating signalsD_(i)(t) for i=0 . . . N in accordance with the present invention cansubstantially reduce or eliminate the effects of noise in the outputsignals Ŝ_(i)(k) and n(k), and can also substantially reduce oreliminate crosstalk between the signals.

As shown in FIG. 17, a set of N+1 signals S_(i)[k] i=1 . . . N, and n(k)are sampled at a rate T/QN, where T is a modulation period. Forsimplicity, the decimation rate R₁ is assumed to be the same as thefactor Q. The assumption that R₁=Q is not a necessary assumption, butrather is used here to simplify the mathematics. The signals arecombined according to the formula:

S(k)=M ₁(k)S ₁(k)+M ₂(k)S ₂(k)+M ₃(k)S ₃(k)+ . . . +M _(N)(k)S_(N)(k)+n(k)  (42)

Using the symbol * to denote the convolution operator, the termsM_(i)(k) are given by:

M ₁(k)=Δ(2Nt/T)*P ₁(t)|_(t=kT/QN)

M ₂(k)=Δ(2Nt/T)*P ₂(t)|_(t=kT/QN)

M _(N)(k)=Δ(2Nt/T)*P _(N)(t)|_(t=kT/QN)  (43)

where $\begin{matrix}{{\Delta \quad (x)} = \left\{ {\begin{matrix}1 & {{{if}\quad {x}} \leq 0.5} \\0 & {otherwise}\end{matrix}{and}} \right.} & (44) \\{{P_{1}(t)} = {\sum\limits_{n = {- \infty}}^{\infty}{\delta \quad \left( {t - {nT}} \right)}}} & (45)\end{matrix}$

(where δ(k) is the Kröneker delta function, which is 1 for k=0, and 0for all other values of k), and $\begin{matrix}{{P_{i}(t)} = {{{P_{1}\left( {t - \frac{\left( {i - 1} \right)T}{N}} \right)}\quad {for}\quad i} = {2\quad \ldots \quad N}}} & (46)\end{matrix}$

After the pre-demodulation and sample rate compression stage 1622, whichdecimates by a factor Q, the signal in the frequency domain is givenapproximately by $\begin{matrix}\begin{matrix}{{{MF}(f)} = \quad {\frac{1}{T}{\sum\limits_{n = {- \infty}}^{\infty}\left\lbrack {{S_{1}\left( {f - \frac{n}{T}} \right)} + {\xi_{1}^{n}{S_{2}\left( {f - \frac{2n}{T}} \right)}} + \ldots \quad +} \right.}}} \\{{\quad \left. {\xi_{N - 1}^{n}{S_{N}\left( {f - \frac{Nn}{T}} \right)}} \right\rbrack} + {\frac{2N}{T}{\sum\limits_{m = {- \infty}}^{\infty}{S_{n}\left( {f - \frac{2{Nm}}{T}} \right)}}}}\end{matrix} & (47)\end{matrix}$

where $\begin{matrix}{\xi_{k}^{n} = ^{\frac{j\quad 2\pi \quad {kn}}{N}}} & (48)\end{matrix}$

The demodulator sequences are then given by: $\begin{matrix}\begin{matrix}{{D_{0}(k)} = \frac{\left( {1 - \left( {- 1} \right)^{k}} \right)}{2}} \\{{D_{1}(k)} = {{P_{1}(k)} - \frac{D_{0}(k)}{N}}} \\{{D_{2}(k)} = {{P_{2}(k)} - \frac{D_{0}(k)}{N}}} \\{\quad \vdots} \\{{D_{N}(k)} = {{P_{N}(k)} - \frac{D_{0}(k)}{N}}}\end{matrix} & (49)\end{matrix}$

where $\begin{matrix}{{{{{{{P_{1}(k)} = {P_{1}(t)}}}_{t = \frac{kT}{2N}},{{P_{2}(k)} = {P_{2}(t)}}}}_{t = \frac{kT}{2N}},\ldots \quad,{{P_{N}(k)} = {P_{N}(t)}}}}_{t = \frac{kT}{2N}} & (50)\end{matrix}$

The post demodulation lowpass filters 1630, 1640, 1720, 1730 and 1740,and the post demodulation sample rate compression stages 1632, 1642,1721, 1731 and 1741 suppress high frequency artifacts which are producedby the modulation/demodulation process. Note that Equation 49 reduces toEquation 40 for N=2.

Adaptive Demodulation

The multi-channel pre-demodulation decimation technique described in theprevious section can be extended to an adaptive multi-channel systemhaving an adjustable pre-demodulation decimation rate and an adjustablepost-demodulation decimation rate. FIG. 18 illustrates an expansion ofthe multichannel modulator into a adaptive multi-channelmodulator/demodulator 1800. FIG. 18 shows the first modulator 191 andthe N^(th) modulator 1702 as shown in FIG. 17. The signal input S₁(t)and a modulation input M₁(t) are provided to the first modulator 191. Asignal input S_(N)(t) and a modulation input M_(N)(t) are provided tothe N^(th) modulator 1702.

The photodetector 150 is modeled as an adder 194 and an adder 196. Theoutputs of the modulators 191, 193, 1701, and 1703 are added together inthe adder 194, to generate a composite signal M(t) where:

M(t)=S ₁(t)M ₁(t)+ . . . +S _(N)(t)M _(N)(t)  (51)

The signal M(t) from the adder 194 is provided to the adder 196 wherethe signal M(t) is added to the signal n(t) which represents a compositenoise signal caused by ambient light, electromagnetic pickup, and thelike, which are also detected by the photodetector 150. The output ofthe adder 196 is the signal M′(t)=M(t)+n(t), which includes noisecomponents as well as the signal components.

The M′(t) signal output of the adder 196 (i.e., the output of thedetector 150) is applied to the input of the signal-processing block1800. Within the signal-processing block 1800, the signal M′(t) is firstpassed through the amplifier 197 and then through the analog bandpassfilter 198. The analog bandpass filter 198 provides anti-aliasing andremoval of low frequency noise and DC. The desired signal components inthe signals S_(i)(t) are frequency shifted by the operation of themodulation signals M_(i)(t) and are passed by the analog bandpass filter198.

The output of the analog bandpass filter 198 is sampled by theanalog-to-digital converter 199 and converted therein to digital signalsand provided to an input of a decimation block 1820. The adaptivedecimation block 1820 comprises a digital lowpass filter and a samplerate compressor that reduces the sample rate by the decimation rate R₁.The filter coefficients and decimation rate R₁ are provided to a controlinput of the adaptive decimation block 1820 by an output of an adaptivealgorithm block 1850. Equation 35 assumes that the decimation rate R₁ isequal to Q. However, in general, the value of Q may be different thanthe decimation rate R₁. The output of the adaptive decimation block 1820is a signal MF(k).

The signal MF(k) is provided to the first input of the first mixer 1624,to the first input of the N ′th mixer 1712, and to the first input ofthe noise channel mixer 1713. A first demodulating signal D₁(k) isprovided to a second input of the first mixer 1624 from a signalgenerator 1841. The fourth demodulating signal D_(N)(k) is provided tothe N^(th) mixer 1712 from an output of a signal generator 1831. Thenoise demodulating signal D₀(k) is provided to the noise channel mixer1713 from an output of a signal generator 1832. A control input to eachof the signal generators 1831, 1832, and 1841 is provided by the outputof the adaptive algorithm 1850. In yet another embodiment, the adaptivealgorithm 1850 may also be controlled by other signal processingelements downstream of the signal processor 1800.

The outputs of the mixers 1713, 1624, and 1712 are provided asrespective inputs to adaptive decimation blocks 1840, 1830, and 1834respectively. Each of the adaptive decimation blocks 1840, 1830, and1834 has a control input provided by the output of the adaptivealgorithm block 1850. The output of the adaptive decimation block 1840is an estimate of the signal n(t) and it is provided to an input of theadaptive algorithm block 1850. In an alternate embodiment, the signalestimates Ŝ_(i)(k) are also provided to the adaptive algorithm block1850.

An output of the decimator 1830 is a signal Ŝ₁(k), which, as discussedabove, is an estimate of the signal S₁(k). Likewise, the output of thedecimation block 1834 is an estimate of the signal S_(N)(t). As shownabove, the selection of the demodulating signals D_(i)(t) for i=0 . . .N in accordance with the present invention substantially reduces oreliminates the effects of noise in the output signals Ŝ_(i)(k) and n(k),and also substantially reduces or eliminates crosstalk between thesignals.

As shown in FIG. 18, a set of N+1 signals S_(i)[k] i=1 . . . N, and n(k)are sampled at a rate T/QN, where T is a modulation period, and R₁ isthe decimation rate of the decimation block 1820. The signals arecombined according to the formula:

S(k)=M ₁(k)S ₁(k)+ . . . +M _(N)(k)S _(N)(k)+n(k)  (52)

Each of the adaptive decimators 1820, 1840, 1830, and 1834 comprises adigital lowpass filter and a sample rate compressor. The characteristicsof the digital lowpass filters (e.g., the number of filter coefficientsand values of the filter coefficients) and the sample rate compressionfactor of each adaptive decimator is provided to a control input of theadaptive decimator. The control inputs are driven by an adaptivealgorithm 1850. The signal generators 1831, 1832 and 1841 generate thedemodulation sequences for the demodulators 1624, 1712, and 1713respectively. The demodulation sequences produced by the signalgenerators 1831, 1832 and 1841 are controlled by the adaptive algorithm1850.

The adaptive algorithm adjusts the pre-demodulation decimation rate R₁(in the adaptive demodulator 1820), and the post-demodulation decimationrate R₂ (in the adaptive demodulators 1830, 1834 and 1840) according tothe noise in the noise estimate {circumflex over (n)}(k) 1746 and(optionally) according to the signals Ŝ_(i)(k). The product R₁R₂ is thetotal decimation rate from the signal S(k) at the output of the A/Dconverter 199 to the signals Ŝ_(i)(k) at the output of the signalprocessing block 1800. The adaptive algorithm may adjust R₁ and R₂ suchthat the product R₁R₂ varies, or the adaptive algorithm may adjust R₁and R₂ such that the product R₁R₂ is substantially constant. Typically,the adaptive algorithm will keep the R₁R₂ product constant so that thesignal processing blocks downstream of the signal processor 1800 willoperate at a substantially constant sample rate.

Typically, each of the signal generators 1841, 1831 and 1832 generates arepeating sequence of numbers. The number of elements in the sequence isa function of the decimation factor R₁. As discussed above in connectionwith FIG. 3, when R₁=1, there are preferably 148 values in eachdemodulation sequence. As discussed above in connection with FIG. 17,when R₁=37, there are preferably only 4 values in the demodulationsequences.

The adaptive algorithm selects R₁, R₂, and the filter transfer functionsin the adaptive decimators 1820, 1830, 1834, and 1840 to improve thequality of the output signals Ŝ_(i)(k). For example, in high ambientnoise environments, the higher order harmonics of the output signals areoften contaminated by ambient noise (as discussed in connection withFIGS. 14 and 20). Thus, the higher order harmonics are preferably notdemodulated when ambient noise is present. To avoid demodulation of thehigher order harmonics the adaptive demodulator 1850 can set R₁=1 andR₂=37, and thereby demodulate according to the method described inconnection with FIGS. 3-14. Alternatively, the adaptive demodulator 1850can set R₁=37, set R₂=1, and set the transfer function of the lowpassfilter in the adaptive decimator 1820 to provide a very fast rolloff(thereby filtering out the higher order harmonics).

Conversely, in low ambient noise environments, the higher orderharmonics of the output signal are less contaminated by ambient noise,and thus the higher order harmonics may be demodulated. In oneembodiment, to demodulate the higher order harmonics, the adaptivedemodulator 1850 can set R₁=37 and set R₂=1, to demodulate according tothe method described in connection with FIG. 17. This is especiallyadvantageous when perfusion is low, because, when perfusion is low theoutput signals Ŝ_(i)(k) are typically very weak and are contaminated byrandom noise. Demodulating more of the higher order harmonics increasesthe signal-to-noise ratio because it adds the harmonics (which arecorrelated) to the output signals, and tends to average out the noise(which is uncorrelated). Thus, the signal strength increases, and thenoise is reduced.

One skilled in the art will recognize that the examples in the precedingtwo paragraphs are merely two points on a continuum and that theadaptive algorithm 1850 can generate many desirable solutions on thecontinuum.

Ambient Light Rejection

In the pulse oximeter, one of the major contributors to the noise signaln(t) is ambient light that is detected by the photodetector 150. Oneaspect of the present invention advantageously provides a method forchoosing the modulation sampling rate f_(s) and the factor Q so that theeffects of ambient light can be removed by the post demodulationfiltering and decimation stages. Note that Q is the number of samplesduring the on period (i.e., modulation signal sample turn on time Q) andis preferably also the decimation rate R₁ for the pre-demodulationsample rate compressor 1622 (in general the values of Q and R₁ may bedifferent). The particular embodiment described by Equation 35 assumesthat the value Q is also used as decimation rate R₁ for thepre-demodulation decimator 1820.

In the system shown in FIGS. 3 and 16, which demodulates two harmonics,the period of a modulation cycle is given by:

T=4Q/f _(s)  (53)

where f_(s) is the sample rate. Defining the two line equations

y(f _(a) ,n)=nf _(a)−1/T

z(f _(a) ,n)=nf _(a)−2/T  (54)

where

f _(a)=line frequencies of concern

n=line frequency harmonic numbers of concern  (55)

then the effects due to ambient light will be minimized when

|y(f _(a) ,n)|≧SBF

|z(f _(a) ,n)|≧SBF  (56)

where SBF is the stop band frequency of the post demodulation anddecimation stages (e.g., the 10 Hz lowpass filter 1630 and the samplerate compressor 1632, etc.).

FIG. 19 is a flowchart showing a method for selecting f_(s) and Q. Themethod begins at a process block 1902 wherein the ambient lightfrequencies f_(a) and important harmonic components n are identified.Important harmonics are defined as those harmonics that will degradesystem performance below acceptable levels when detected by the detector150. The process then advances from the process block 1902 to a processblock 1904. In the process block 1904, the values of f_(a) and nidentified in the process block 1902 are used in conjunction withEquation 54 to identify a collection of acceptable values of T. Uponcompletion of the process block 1904, the process advances to a processblock 1906. In the process 1906, suitable values of f_(s) and Q arechosen using the values of T obtained in the process block 1904 and theequation T=4Q/f_(s). One skilled in the art will recognize that, since Tis proportional to the ratio of Q/f_(s), knowing T will not uniquelydetermine either f_(s) or Q.

For example, given power line frequencies of 50±1 Hz and 60±1 Hz thenthe range of f_(a) is given by approximately the union of the interval49-51 Hz and the interval 59-61 Hz, which can be expressedmathematically as:

f _(a)≈[49,51]∪[59,61]  (57)

Assuming that all harmonics up to the 18^(th) harmonic are to besuppressed, then n=1 . . . 18. In a preferred embodiment, using thesevalues for f_(a) and n, application of the method in FIG. 19 results inf_(s)=46,875 Hz and acceptable Q values of 37 and 41.

The process leading to Equation 57 is illustrated graphically by FIG.20, where the harmonics of the ambient light frequency f_(a) (in Hz) areplotted versus the plethysmograph signal frequency (also in Hz). FIG. 20has an x-axis showing the ambient light frequency from 44 Hz to 64 Hz.The ambient light frequency will usually correspond to the frequency ofthe power lines, which is nominally 60 Hz (in the U.S.) and 50 Hz(outside the U.S.). However, power line frequency regulation typicallyvaries somewhat, and thus FIG. 20 shows frequencies above and below thenominal frequencies.

FIG. 20 also shows a y-axis showing the plethysmograph signal frequencyfrom −10 Hz to 10 Hz. One skilled in the art will recognize thatnegative frequencies occur in the mathematics described above. Inparticular, a signal that is modulated from baseband up to some carrierfrequency will exhibit two sidebands, a sideband above the carrierfrequency corresponding to the frequency of the baseband signal, and asideband below the carrier frequency corresponding to the negative ofthe baseband frequency. Thus, when dealing with modulation anddemodulation, it is convenient to deal with positive and negativefrequencies.

FIG. 20 also shows harmonic lines corresponding to the 5^(th), 6^(th),7^(th), 10^(th), 11^(th), 12^(th), 13^(th), and 14^(th) harmonics of theambient light frequency. The harmonic lines correspond to the harmonicsproduced in the plethysmograph signal by the demodulation (mixing down)of harmonics of the power line frequency. The lines in FIG. 20 arecalculated using Equation 54 for 1/T=316.72 Hz. Some of the harmoniclines correspond to y(f_(a),n) and some correspond to z(f_(a),n) fromEquation 54. Harmonic lines that are not shown (e.g., the linecorresponding to the 8^(th) harmonic) fall outside the displayed limitsof the x-axis and y-axis.

FIG. 20 can be used to determine the stop band frequencies as shown inEquation 56. For example, the harmonic lines in FIG. 20 show that for anambient light frequency of 49 Hz, the 13^(th) harmonic of the ambientlight frequency will appear in the plethysmograph signal atapproximately 3 Hz. Thus, FIG. 20 shows that for plethysmographbandwidth of 10 Hz, none of the first 14 harmonics of the ambient lightwill appear in the plethysmograph signal for ambient light frequenciesbetween approximately 61.2 Hz and approximately 58.5 Hz, which isconsistent with Equation 57. The first ambient harmonics that do appearfor a plethysmograph bandwidth of 10 Hz are the 5^(th) harmonic and the11^(th) harmonic.

Other Embodiments

In the preferred embodiment of the present invention, the hardwaredescribed above is implemented in a digital signal processor andassociated circuitry. The LED modulation block 104 and the LEDdemodulation state table block 352 comprise algorithms implemented byprogram code executed by the digital signal processor. In addition, theconfiguration variables, such as for example, the hardware delay value,the hardware distortion value and the hardware scale value are providedas inputs to the digital signal processor when it is set up. Forexample, the main operating program of the digital signal processor maybe stored in non-volatile ROM or PROM, and the variables may be storedin flash memory during a setup procedure. Techniques for communicatingto and from a digital signal processor during such setup procedures arewell known to persons of skill in the art, and will not be described indetail herein. For example, the configuration bus 310, discussed above,represents a communication path to the flash memory during such a setupprocedure. The data provided to the configuration bus 310 may beprovided by a system operator (not shown) or the data may be providedfrom look-up tables (not shown) maintained for different embodiments ofthe LEDs 106, 108 and the detector 150.

Although described above in connection with a pulse oximetry systemwherein a parameter to be measured is the attenuation of red andinfrared light passing through a portion of a subject's body, it shouldbe understood that the method and apparatus described herein can also beused for other measurements where two or more signals are passed througha system to be analyzed. In particular, the present invention can beused to demodulate two combined parametric signals responsive to thesystem to be analyzed where the two parametric signals have apredetermined timing relationship between them, as described herein.

One skilled in the art will recognize that the lowpass filters providedin connection with the decimation blocks may provide other filterfunctions in addition to lowpass filtering. Thus, for example, thelowpass filters 1620, 1622, 1630, 1640, 1650, 1720, 1730, and 1740, andthe decimators 1820, 1830, 1834, and 1840 may provide other filterfunctions (in addition to lowpass filtering) such as, for example,bandpass filtering, bandstop filtering, etc. Moreover, thepost-demodulation decimation rate R₂ need not be the same for eachoutput channel. Thus, for example, in FIG. 18, the decimator 1840 mayhave a first decimation rate R₂=r₁ while the decimators 1830 and 1834have a second decimation rate R₂=r₂.

Although described above in connection with a particular embodiment ofthe present invention, it should be understood the description of theembodiment is illustrative of the invention and are not intended to belimiting. Various modifications and applications may occur to thoseskilled in the art without departing from the true spirit and scope ofthe invention as defined in the appended claims.

What is claimed is:
 1. A method of demodulating a composite signalgenerated by applying a plurality of periodic pulse trains ofelectromagnetic energy to a system having a parameter to be measured andby receiving signals responsive to said electromagnetic energy afterhaving passed through said system and being affected by said parameterbeing measured, said signals receiving as a composite signal havingcomponents responsive to said plurality of periodic pulse trains, eachof said components corresponding to one each of said pulse trains, saidmethod comprising the steps of: sampling said composite signal using ananalog to digital converter to produce a sequence of digital values;decimating said sequence of digital values to produce a decimatedsequence of values; providing said decimated sequence of values to afirst input of each multiplier in a plurality of multipliers; providinga plurality of sequences of demodulation coefficients to a second inputof each of said multipliers such that each multiplier is provided aunique sequence of demodulation coefficients, each of said sequencesconfigured to demodulate a selected frequency portion of said compositesignal; and lowpass filtering the output of each of said multiplierssuch that the output signal of each of said lowpass filtersapproximately corresponds to one each of said components.
 2. The methodof claim 1, wherein each of said sequences comprises a sampled datarepresentation of a demodulation signal comprising a selected set ofharmonics.
 3. The method of claim 1, wherein each of said sequencescomprises a sampled data representation of an analog demodulation signalcomprising a selected number of harmonics.
 4. The method of claim 3,wherein said sampled data representation is generated by a softwarealgorithm.
 5. The method of claim 1, wherein each of said sequencescorresponds to a demodulation signal comprising a selected set oflow-order harmonics.
 6. The method of claim 5, wherein said low-orderharmonics are selected to avoid demodulating harmonics of said compositesignal that are contaminated by noise.
 7. The method of claim 1, whereineach of said sequences is a time-shifted replica of a defined sequence.8. The method of claim 1, wherein each of said sequences describes aplurality of selected harmonics of said composite signal.
 9. The methodof claim 1, wherein each of said sequences describes a plurality oflow-order harmonics of said composite signal.
 10. An apparatus fordemodulating a multi-channel composite signal comprising: a sequencegenerator for generating a band-limited demodulation sequence, saiddemodulation sequence comprising a plurality of harmonics of a carrierfrequency to demodulate a composite signal modulated by said carrier;and a demodulator having a first input for receiving said demodulationsequence, a second input for receiving said composite signal, and anoutput to provide a demodulated signal.
 11. An apparatus fordemodulating a multi-channel composite signal comprising: a sequencegenerator for generating a demodulation sequence, said demodulationsequence comprising a plurality of harmonics of a composite signal todemodulate said harmonics of said composite signal; demodulator meansfor demodulating said composite signal, by using said demodulationsequence, to produce a demodulated signal.
 12. The apparatus of claim11, wherein said demodulation sequence is configured to avoiddemodulating undesired frequency components of said composite signal.13. The apparatus of claim 11, further comprising means for filteringand decimating said demodulated signal.
 14. The apparatus of claim 11,further comprising means for adaptively filtering and decimating saiddemodulated signal.